Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2015, Volume 143, Issue 1, pp. 301 - 308

G. Godefroy and the second author of this note proved in 1988 that in duals to Asplund spaces there always exists a projectional resolution of the identity. A...

Projectional resolution of identity | Projectional skeleton | Weak star dentability | Asplund space | Jayne-Rogers selection theorem | Separable reduction | projectional resolution of identity | MATHEMATICS | MATHEMATICS, APPLIED | separable reduction | RESOLUTION | projectional skeleton | weak star dentability | Mathematics - Functional Analysis

Projectional resolution of identity | Projectional skeleton | Weak star dentability | Asplund space | Jayne-Rogers selection theorem | Separable reduction | projectional resolution of identity | MATHEMATICS | MATHEMATICS, APPLIED | separable reduction | RESOLUTION | projectional skeleton | weak star dentability | Mathematics - Functional Analysis

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 11/2014, Volume 142, Issue 11, pp. 3933 - 3939

A typical result in this note is that if X- \omega is already an Asplund space.

Unit ball | Series convergence | Mathematical sequences | Mathematical theorems | Applied mathematics | Mathematical functions | Topology | Banach space | Lurs | Separable complementation property | SCP | Weak-star-to-weak Kadets Klee property | Grothendieck spaces | Renormings | Weak-star Kadets Klee property | Coseparable subspaces | Asplund spaces | Duality mapping | Weakly Lindelöf determined | WLD | MATHEMATICS, APPLIED | renormings | duality mapping | coseparable subspaces | MATHEMATICS | weak-star Kadets Klee property | BANACH-SPACES | weakly Lindelof determined | separable complementation property | weak-star-to-weak Kadets Klee property

Unit ball | Series convergence | Mathematical sequences | Mathematical theorems | Applied mathematics | Mathematical functions | Topology | Banach space | Lurs | Separable complementation property | SCP | Weak-star-to-weak Kadets Klee property | Grothendieck spaces | Renormings | Weak-star Kadets Klee property | Coseparable subspaces | Asplund spaces | Duality mapping | Weakly Lindelöf determined | WLD | MATHEMATICS, APPLIED | renormings | duality mapping | coseparable subspaces | MATHEMATICS | weak-star Kadets Klee property | BANACH-SPACES | weakly Lindelof determined | separable complementation property | weak-star-to-weak Kadets Klee property

Journal Article

Journal of Operator Theory, ISSN 0379-4024, 10/2012, Volume 68, Issue 2, pp. 405 - 442

For α an ordinal, we investigate the class 𝒮𝓛α consisting of all operators whose Szlenk index is an ordinal not exceeding ωα. We show that each class 𝒮𝓛α...

Logical proofs | Separable spaces | Counterexamples | Topology | Banach space | Factorization | Cofinality | Operator theory | Induction assumption | Asplund operator | Factorization property | Operator ideal | Space ideal | Szlenk index | INTERPOLATION | MATHEMATICS | operator ideal | UNIVERSAL | BANACH-SPACES | WEAK-ASTERISK | COMPACT-OPERATORS | factorization property | space ideal | RENORMINGS

Logical proofs | Separable spaces | Counterexamples | Topology | Banach space | Factorization | Cofinality | Operator theory | Induction assumption | Asplund operator | Factorization property | Operator ideal | Space ideal | Szlenk index | INTERPOLATION | MATHEMATICS | operator ideal | UNIVERSAL | BANACH-SPACES | WEAK-ASTERISK | COMPACT-OPERATORS | factorization property | space ideal | RENORMINGS

Journal Article

Mathematical Programming, ISSN 0025-5610, 1/2009, Volume 116, Issue 1, pp. 397 - 427

In this paper, using the Fréchet subdifferential, we derive several sufficient conditions ensuring an error bound for inequality systems in Asplund spaces. As...

Mathematical and Computational Physics | Mathematics | Mathematical Methods in Physics | 90C30 | Asplund space | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 49J52 | Numerical Analysis | Fuzzy calculus | Error bounds | Metric regularity | Combinatorics | MATHEMATICS, APPLIED | SUBDIFFERENTIAL CALCULUS | OPTIMIZATION PROBLEMS | error bounds | WEAK SHARP MINIMA | DIFFERENTIABILITY | fuzzy calculus | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | metric regularity | LINEAR REGULARITY | POINTS | Fuzzy logic | Studies | Calculus | Mathematical analysis | Mathematical programming

Mathematical and Computational Physics | Mathematics | Mathematical Methods in Physics | 90C30 | Asplund space | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 49J52 | Numerical Analysis | Fuzzy calculus | Error bounds | Metric regularity | Combinatorics | MATHEMATICS, APPLIED | SUBDIFFERENTIAL CALCULUS | OPTIMIZATION PROBLEMS | error bounds | WEAK SHARP MINIMA | DIFFERENTIABILITY | fuzzy calculus | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | metric regularity | LINEAR REGULARITY | POINTS | Fuzzy logic | Studies | Calculus | Mathematical analysis | Mathematical programming

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 6/2011, Volume 83, Issue 3, pp. 450 - 455

A Banach space is an Asplund space if every continuous gauge has a point where the subdifferential mapping is Hausdorff weak upper semi-continuous with weakly...

gauge | polar | Radon-Nikodým property | Fréchet differentiability | subdifferential mapping | extreme point | weak upper semi-continuity | MATHEMATICS | UPPER SEMI-CONTINUITY | DUALITY MAPPINGS | NORM | Radon-Nikodym property | Frechet differentiability

gauge | polar | Radon-Nikodým property | Fréchet differentiability | subdifferential mapping | extreme point | weak upper semi-continuity | MATHEMATICS | UPPER SEMI-CONTINUITY | DUALITY MAPPINGS | NORM | Radon-Nikodym property | Frechet differentiability

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2006, Volume 134, Issue 9, pp. 2745 - 2754

In this paper we construct a Gâteaux differentiability space that is not a weak Asplund space. Thus we answer a question raised by David Larman and Robert...

Unit ball | Topological theorems | Homeomorphism | Differential topology | Mathematical functions | Metric spaces | Topology | Banach space | Topological spaces | Weak Asplund space | Gâteaux differentiability space | Stegall space | MATHEMATICS | MATHEMATICS, APPLIED | Gateaux differentiability space | weak Asplund space

Unit ball | Topological theorems | Homeomorphism | Differential topology | Mathematical functions | Metric spaces | Topology | Banach space | Topological spaces | Weak Asplund space | Gâteaux differentiability space | Stegall space | MATHEMATICS | MATHEMATICS, APPLIED | Gateaux differentiability space | weak Asplund space

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2006, Volume 65, Issue 3, pp. 660 - 676

In this paper, we study a new concept of weak regularity of functions and sets in Asplund spaces. We show that this notion includes prox-regular functions,...

Weak regularity | Mordukhovich regularity | Subdifferentials | Weak submonotonicity | Epi-Lipschitz sets | Amenability | NONSMOOTH ANALYSIS | HILBERT-SPACES | MATHEMATICS, APPLIED | weak regularity | CALMNESS | MULTIFUNCTIONS | weak submonotonicity | amenability | epi-Lipschitz sets | MATHEMATICS | FINITE | DIFFERENTIALS | CONSTRAINTS | VARIATIONAL ANALYSIS | subdifferentials

Weak regularity | Mordukhovich regularity | Subdifferentials | Weak submonotonicity | Epi-Lipschitz sets | Amenability | NONSMOOTH ANALYSIS | HILBERT-SPACES | MATHEMATICS, APPLIED | weak regularity | CALMNESS | MULTIFUNCTIONS | weak submonotonicity | amenability | epi-Lipschitz sets | MATHEMATICS | FINITE | DIFFERENTIALS | CONSTRAINTS | VARIATIONAL ANALYSIS | subdifferentials

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2005, Volume 133, Issue 2, pp. 425 - 429

Assuming the consistency of the existence of a measurable cardinal, it is consistent to have two Banach spaces, X,Y, where X is a weak Asplund space such that...

Mathematical set theory | Mathematical theorems | Kalinda | Axioms | Mathematical analysis | Mathematical functions | Banach space | Topological spaces | Weak Asplund space | Fragmentable space | Measurable cardinal | Stegall's class of spaces | MATHEMATICS | measurable cardinal | MATHEMATICS, APPLIED | weak Asplund space | COHEN EXTENSIONS | fragmentable space | PRECIPITOUS IDEALS

Mathematical set theory | Mathematical theorems | Kalinda | Axioms | Mathematical analysis | Mathematical functions | Banach space | Topological spaces | Weak Asplund space | Fragmentable space | Measurable cardinal | Stegall's class of spaces | MATHEMATICS | measurable cardinal | MATHEMATICS, APPLIED | weak Asplund space | COHEN EXTENSIONS | fragmentable space | PRECIPITOUS IDEALS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2013, Volume 405, Issue 1, pp. 297 - 309

In this article, we begin using some geometric methods to study the isometric extension problem in general real Banach spaces. For any Banach space Y, we...

Asplund generated space | Weak∗-exposed point | Isometric extension | Weak-Asplund space | Sharp corner point | Weakly compactly generated space | Gâteaux differentiable space | Weak | exposed point | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | L-INFINITY | MATHEMATICS | Weak-exposed point | P-SPACES | NORMED SPACE | Gateaux differentiable space | REPRESENTATION THEOREM | HILBERT-SPACE | 2 UNIT SPHERES

Asplund generated space | Weak∗-exposed point | Isometric extension | Weak-Asplund space | Sharp corner point | Weakly compactly generated space | Gâteaux differentiable space | Weak | exposed point | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | L-INFINITY | MATHEMATICS | Weak-exposed point | P-SPACES | NORMED SPACE | Gateaux differentiable space | REPRESENTATION THEOREM | HILBERT-SPACE | 2 UNIT SPHERES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2016, Volume 434, Issue 1, pp. 182 - 190

In this paper, author proves that if X1 and X2 are Gâteaux differentiable space, then X1 and X2 have the ball-covering property if and only if (X1×X2,‖⋅‖p) and...

Gâteaux differentiable space | Ball-covering property | Convex function | MATHEMATICS | MATHEMATICS, APPLIED | MAPPINGS | WEAK ASPLUND SPACES | Gateaux differentiable space | CONVEX-FUNCTIONS | FRECHET DIFFERENTIABILITY | Bisphenol-A

Gâteaux differentiable space | Ball-covering property | Convex function | MATHEMATICS | MATHEMATICS, APPLIED | MAPPINGS | WEAK ASPLUND SPACES | Gateaux differentiable space | CONVEX-FUNCTIONS | FRECHET DIFFERENTIABILITY | Bisphenol-A

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2001, Volume 129, Issue 12, pp. 3741 - 3747

Under the assumption that there exists in the unit interval [0,1] an uncountable set A with the property that every continuous mapping from a Baire metric...

Unit ball | Topological theorems | Homeomorphism | Mathematical functions | Topology | Banach space | Topological spaces | Continuous functions | Weak asplund space | Baire space | Double arrow space | Stegall's class | Minimal usco | Fragmentability | fragmentability | MATHEMATICS | MATHEMATICS, APPLIED | weak Asplund space | double arrow space | minimal usco

Unit ball | Topological theorems | Homeomorphism | Mathematical functions | Topology | Banach space | Topological spaces | Continuous functions | Weak asplund space | Baire space | Double arrow space | Stegall's class | Minimal usco | Fragmentability | fragmentability | MATHEMATICS | MATHEMATICS, APPLIED | weak Asplund space | double arrow space | minimal usco

Journal Article

Topology and its Applications, ISSN 0166-8641, 2012, Volume 159, Issue 1, pp. 183 - 193

Let ( X , τ ) be a topological space and let ρ be a metric defined on X. We shall say that ( X , τ ) is fragmented by ρ if whenever ε > 0 and A is a nonempty...

Fragmentable | σ-Fragmentable | Function spaces | Topological groups | MATHEMATICS, APPLIED | NORMS | WEAK ASPLUND | MATHEMATICS | CONTINUITY | SIGMA-FRAGMENTABILITY | CONTINUOUS-MAPPINGS | sigma-Fragmentable | BANACH-SPACES | RADON-NIKODYM PROPERTY | SETS | OPTIMIZATION | ASPLUND SPACES

Fragmentable | σ-Fragmentable | Function spaces | Topological groups | MATHEMATICS, APPLIED | NORMS | WEAK ASPLUND | MATHEMATICS | CONTINUITY | SIGMA-FRAGMENTABILITY | CONTINUOUS-MAPPINGS | sigma-Fragmentable | BANACH-SPACES | RADON-NIKODYM PROPERTY | SETS | OPTIMIZATION | ASPLUND SPACES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 371, Issue 2, pp. 425 - 435

We study binormality, a separation property of the norm and weak topologies of a Banach space. We show that every Banach space which belongs to a P -class is...

[formula omitted]-class | Weak topology | Asplund space | Banach space | Binormality | P-class | MATHEMATICS | MATHEMATICS, APPLIED

[formula omitted]-class | Weak topology | Asplund space | Banach space | Binormality | P-class | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/2002, Volume 130, Issue 7, pp. 2139 - 2143

We show that, under some additional set-theoretical assumptions which are equiconsistent with the existence of a measurable cardinal, there is a weak Asplund...

Mathematical theorems | Kalinda | Martins axiom | Mathematics | Mathematical functions | Local extrema | Banach space | Continuum hypothesis | Topological spaces | Continuous functions | Weak Asplund space | Fragmentable space | Stegall's class of spaces | MATHEMATICS | MATHEMATICS, APPLIED | weak Asplund space | fragmentable space

Mathematical theorems | Kalinda | Martins axiom | Mathematics | Mathematical functions | Local extrema | Banach space | Continuum hypothesis | Topological spaces | Continuous functions | Weak Asplund space | Fragmentable space | Stegall's class of spaces | MATHEMATICS | MATHEMATICS, APPLIED | weak Asplund space | fragmentable space

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 04/2015, Volume 91, Issue 2, pp. 303 - 310

In a recent paper, topological spaces (X, tau) that are fragmented by a metric that generates the discrete topology were investigated. In the present paper we...

Fragmentable | Sigma-scattered | Topological game | WEAK ASPLUND SPACE | MATHEMATICS | sigma-scattered | CONTINUITY | SIGMA-FRAGMENTABILITY | CONTINUOUS-MAPPINGS | BANACH-SPACES | RADON-NIKODYM PROPERTY | NORM | OPTIMIZATION | DIFFERENTIATION | fragmentable | topological game

Fragmentable | Sigma-scattered | Topological game | WEAK ASPLUND SPACE | MATHEMATICS | sigma-scattered | CONTINUITY | SIGMA-FRAGMENTABILITY | CONTINUOUS-MAPPINGS | BANACH-SPACES | RADON-NIKODYM PROPERTY | NORM | OPTIMIZATION | DIFFERENTIATION | fragmentable | topological game

Journal Article

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ESSENTIAL SMOOTHNESS, ESSENTIAL STRICT CONVEXITY, AND LEGENDRE FUNCTIONS IN BANACH SPACES

Communications in Contemporary Mathematics, ISSN 0219-1997, 11/2001, Volume 3, Issue 4, pp. 615 - 647

The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions are extended from Euclidean to Banach spaces....

Convex function of Legendre type | Bregman distance, Bregman projection | Cofinite function | Schur property | Schur space | Subdifferential | Weak Asplund space | Essentially smooth | Essentially strictly convex | Legendre function | Supercoercive | Coercive | MATHEMATICS, APPLIED | weak Asplund space | cofinite function | zone consistent | convex function of Legendre type | essentially strictly convex | Bregman distance | supercoercive | Bregman projection | MATHEMATICS | subdifferential | essentially smooth | coercive | Mathematical optimization | Analysis | Algorithms

Convex function of Legendre type | Bregman distance, Bregman projection | Cofinite function | Schur property | Schur space | Subdifferential | Weak Asplund space | Essentially smooth | Essentially strictly convex | Legendre function | Supercoercive | Coercive | MATHEMATICS, APPLIED | weak Asplund space | cofinite function | zone consistent | convex function of Legendre type | essentially strictly convex | Bregman distance | supercoercive | Bregman projection | MATHEMATICS | subdifferential | essentially smooth | coercive | Mathematical optimization | Analysis | Algorithms

Journal Article

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, ISSN 1345-4773, 2017, Volume 18, Issue 10, pp. 1867 - 1882

In this paper, some necessary and sufficient conditions for Gateaux differentiability of w*-lower semicontinuous convex function of X** are given. Moreover, we...

MATHEMATICS | MATHEMATICS, APPLIED | Asplund space | ball-covering property | WEAK ASPLUND | convex function | FRECHET DIFFERENTIABILITY | Gateaux differentiability

MATHEMATICS | MATHEMATICS, APPLIED | Asplund space | ball-covering property | WEAK ASPLUND | convex function | FRECHET DIFFERENTIABILITY | Gateaux differentiability

Journal Article

Journal of Convex Analysis, ISSN 0944-6532, 2011, Volume 18, Issue 2, pp. 433 - 446

The theme of this paper is the study of the separability of subspaces of holomorphic functions respect to the convergence over a given set and its connection...

Asplund set | Interpolation | Algebras of analytic functions | Radon-Nikodým property | Polynomial topology | Composition operator | polynomial topology | MATHEMATICS | WEAK COMPACTNESS | composition operator | interpolation | CONVERGENCE | Radon-Nikodym property | HOLOMORPHIC MAPPINGS | REFLEXIVE BANACH-SPACES | ANALYTIC-FUNCTIONS

Asplund set | Interpolation | Algebras of analytic functions | Radon-Nikodým property | Polynomial topology | Composition operator | polynomial topology | MATHEMATICS | WEAK COMPACTNESS | composition operator | interpolation | CONVERGENCE | Radon-Nikodym property | HOLOMORPHIC MAPPINGS | REFLEXIVE BANACH-SPACES | ANALYTIC-FUNCTIONS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2003, Volume 197, Issue 1, pp. 1 - 13

We prove that a dual Banach space X ∗ has an equivalent W ∗ LUR norm if and only if the weak ∗ topology has a σ-isolated network. We give sufficient conditions...

Sigma-isolated network | Weak locally uniformly rotund norms | Weak Asplund Banach spaces | Smooth renorming of Banach spaces | Fragmentable and descriptive spaces | MATHEMATICS | weak locally uniformly rotund norms | weak Asplund Banach spaces | sigma-isolated network | smooth renorming of Banach spaces | BANACH-SPACES | fragmentable and descriptive spaces

Sigma-isolated network | Weak locally uniformly rotund norms | Weak Asplund Banach spaces | Smooth renorming of Banach spaces | Fragmentable and descriptive spaces | MATHEMATICS | weak locally uniformly rotund norms | weak Asplund Banach spaces | sigma-isolated network | smooth renorming of Banach spaces | BANACH-SPACES | fragmentable and descriptive spaces

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2003, Volume 131, Issue 2, pp. 647 - 654

A topological space X is said to belong to the class of Stegall (weakly Stegall) spaces if for every Baire (complete metric) space B and minimal usco...

Topological theorems | Abstract spaces | Completely regular spaces | Compactification | Metric spaces | Mathematical functions | Topology | Banach space | Topological spaces | Weak Asplund | Weakly Stegall space | Almost weak Asplund | Stegall space | MATHEMATICS | almost weak Asplund | MATHEMATICS, APPLIED | weak Asplund | weakly Stegall space

Topological theorems | Abstract spaces | Completely regular spaces | Compactification | Metric spaces | Mathematical functions | Topology | Banach space | Topological spaces | Weak Asplund | Weakly Stegall space | Almost weak Asplund | Stegall space | MATHEMATICS | almost weak Asplund | MATHEMATICS, APPLIED | weak Asplund | weakly Stegall space

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