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Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2015, Volume 143, Issue 1, pp. 301 - 308
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
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
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
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
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
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2013, Volume 405, Issue 1, pp. 297 - 309
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
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
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
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
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
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
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
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
Journal Article
by Raja, M
Journal of Functional Analysis, ISSN 0022-1236, 2003, Volume 197, Issue 1, pp. 1 - 13
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
Journal Article
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