Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2017, Volume 447, Issue 2, pp. 834 - 845

Given any compact, Hausdorff space K and 1

Szlenk index | Dentability index | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | WEAK-ASTERISK

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2017, Volume 145, Issue 4, pp. 1685 - 1698

We prove a formula for the Szlenk power type of the injective tensor product of Banach spaces with Szlenk index at most \omega . We also show that the Szlenk...

Szlenk power type | Szlenk index | Direct sum | Injective tensor product | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-ASTERISK | injective tensor product | direct sum | INDEX

Szlenk power type | Szlenk index | Direct sum | Injective tensor product | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-ASTERISK | injective tensor product | direct sum | INDEX

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 01/2017, Volume 272, Issue 2, pp. 498 - 521

We study the general measures of non-compactness defined on subsets of a dual Banach space, their associated derivations and their ω-iterates. We introduce the...

Measure of non-compactness | Szlenk index | Renorming Banach spaces | MATHEMATICS | BANACH-SPACES | WEAK-ASTERISK | DENTABILITY INDEX | Functional Analysis | Mathematics

Measure of non-compactness | Szlenk index | Renorming Banach spaces | MATHEMATICS | BANACH-SPACES | WEAK-ASTERISK | DENTABILITY INDEX | Functional Analysis | Mathematics

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2014, Volume 142, Issue 8, pp. 2747 - 2762

Recently, Lima and Randrianarivony pointed out the role of the property (\beta ) of the domain space. We also provide conditions under which this comparison...

Geometry | Separable spaces | Convexity | Banach space | Quotients | Homeomorphism | MATHEMATICS | SZLENK INDEXES | MATHEMATICS, APPLIED | PROPERTY M | WEAK-ASTERISK | BETA

Geometry | Separable spaces | Convexity | Banach space | Quotients | Homeomorphism | MATHEMATICS | SZLENK INDEXES | MATHEMATICS, APPLIED | PROPERTY M | WEAK-ASTERISK | BETA

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2017, Volume 111, Issue 1, pp. 101 - 113

We extend to the non separable setting many characterizations of the Banach spaces admitting an equivalent norm with the property $$(\beta )$$ ( β ) of...

46T99 | Theoretical, Mathematical and Computational Physics | 46B20 | Mathematics, general | Mathematics | Applications of Mathematics | 46B80 | MATHEMATICS | SZLENK INDEX | BANACH-SPACES | WEAK-ASTERISK | BETA | Norms | Texts | Equivalence | Banach space | Asymptotic properties

46T99 | Theoretical, Mathematical and Computational Physics | 46B20 | Mathematics, general | Mathematics | Applications of Mathematics | 46B80 | MATHEMATICS | SZLENK INDEX | BANACH-SPACES | WEAK-ASTERISK | BETA | Norms | Texts | Equivalence | Banach space | Asymptotic properties

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2013, Volume 398, Issue 2, pp. 867 - 871

We prove that if Y is a closed subspace of a Banach space X such that Y and X/Y admit an equivalent asymptotically uniformly smooth norm, then X also admits an...

Three-space property | Asymptotically uniformly smooth norm | Szlenk index | Renorming theory | Geometry of Banach spaces | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | WEAK-ASTERISK | Reforming theory

Three-space property | Asymptotically uniformly smooth norm | Szlenk index | Renorming theory | Geometry of Banach spaces | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | WEAK-ASTERISK | Reforming theory

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

Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2019, Volume 371, Issue 3, pp. 1509 - 1546

We extend a precise renorming result of Godefroy, Kalton, and Lancien regarding asymptotically uniformly smooth norms of separable Banach spaces with Szlenk...

MATHEMATICS | Asplund operators | renorming | WEAK-ASTERISK | asymptotic uniform convexity | asymptotic uniform smoothness | SZLENK INDEX

MATHEMATICS | Asplund operators | renorming | WEAK-ASTERISK | asymptotic uniform convexity | asymptotic uniform smoothness | SZLENK INDEX

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2013, Volume 399, Issue 2, pp. 559 - 564

Let α be an infinite ordinal and γ the unique ordinal satisfying ωωγ≤α<ωωγ+1. We show that the Banach space C([0,α]) of all continuous scalar-valued functions...

Szlenk index | Dentability index | MATHEMATICS | MATHEMATICS, APPLIED | QUOTIENTS | WEAK-ASTERISK

Szlenk index | Dentability index | MATHEMATICS | MATHEMATICS, APPLIED | QUOTIENTS | WEAK-ASTERISK

Journal Article

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, ISSN 0024-6093, 04/2014, Volume 46, Issue 2, pp. 415 - 424

We find an optimal upper bound on the values of the weak*-dentability index Dz(X) in terms of the Szlenk index Sz(X) of a Banach space X with separable dual....

SEPARABLE BANACH-SPACES | MATHEMATICS | WEAK-ASTERISK | DENTABILITY INDEX

SEPARABLE BANACH-SPACES | MATHEMATICS | WEAK-ASTERISK | DENTABILITY INDEX

Journal Article

Canadian journal of mathematics, ISSN 0008-414X, 12/1993, Volume 45, Issue 6, pp. 1121 - 1134

We study the relationships between Gateaux, Fréchet and weak Hadamard differentiability of convex functions and of equivalent norms. As a consequence we...

MATHEMATICS | WEAK-ASTERISK KADEC PROPERTY | GATEAUX DIFFERENTIABILITY | WEAK HADAMARD DIFFERENTIABILITY | RENORMING | (NOT)CONTAINING L1 | CONVEX FUNCTIONS | FRECHET DIFFERENTIABILITY | NONCOMPACT OPERATORS

MATHEMATICS | WEAK-ASTERISK KADEC PROPERTY | GATEAUX DIFFERENTIABILITY | WEAK HADAMARD DIFFERENTIABILITY | RENORMING | (NOT)CONTAINING L1 | CONVEX FUNCTIONS | FRECHET DIFFERENTIABILITY | NONCOMPACT OPERATORS

Journal Article

Journal of Multivariate Analysis, ISSN 0047-259X, 1994, Volume 51, Issue 2, pp. 252 - 264

Uniform convergence of probability measures is analyzed by topologizing the space of events. A new characterization of narrow (weak) convergence of probability...

Glivenko-Cantelli lemma | Narrow (weak, weak) convergence | STATISTICS & PROBABILITY | GLIVENKO-CANTELLI LEMMA | NARROW (WEAK, WEAK-ASTERISK) CONVERGENCE

Glivenko-Cantelli lemma | Narrow (weak, weak) convergence | STATISTICS & PROBABILITY | GLIVENKO-CANTELLI LEMMA | NARROW (WEAK, WEAK-ASTERISK) CONVERGENCE

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 5/1995, Volume 123, Issue 5, pp. 1431 - 1435

Functions into duals and pre-duals of weakly compactly generated spaces (WCG) are studied. We show that a universally weakly measurable function f into a dual...

Hausdorff spaces | Property titles | Radon | Mathematical integrals | Separable spaces | Mathematical functions | Banach space | Weak integral | Universally weakly measurable | Pettis integral | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-ASTERISK INTEGRAL | PETTIS INTEGRAL | UNIVERSALLY WEAKLY MEASURABLE

Hausdorff spaces | Property titles | Radon | Mathematical integrals | Separable spaces | Mathematical functions | Banach space | Weak integral | Universally weakly measurable | Pettis integral | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-ASTERISK INTEGRAL | PETTIS INTEGRAL | UNIVERSALLY WEAKLY MEASURABLE

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 3/1992, Volume 330, Issue 1, pp. 401 - 418

A weakly measurable function f: Ω → X is said to be determined by a subspace D of X if for each x ∈ X , x ∣ = 0 implies that x f = 0 a.e. For a given Dunford...

Integers | Mathematical theorems | Mathematical integrals | Exhaustion | Indefinite integrals | Separable spaces | Integrable functions | Mathematical functions | Banach space | Weak∗ integral | Weak measurability | Pettis integral | MATHEMATICS | WEAK MEASURABILITY | PETTIS INTEGRAL | WEAK-ASTERISK INTEGRAL | BANACH SPACE

Integers | Mathematical theorems | Mathematical integrals | Exhaustion | Indefinite integrals | Separable spaces | Integrable functions | Mathematical functions | Banach space | Weak∗ integral | Weak measurability | Pettis integral | MATHEMATICS | WEAK MEASURABILITY | PETTIS INTEGRAL | WEAK-ASTERISK INTEGRAL | BANACH SPACE

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 6/1993, Volume 337, Issue 2, pp. 609 - 624

Let T be a metric space and X a Banach space. Let be a set-valued map assuming arbitrary values and satisfying the upper semicontinuity condition: is closed...

Topological theorems | Mathematical theorems | Mathematical constants | Mathematical functions | Metric spaces | Topology | Banach space | Topological spaces | Continuous functions | Weak and weak | Selectors | Baire class 1 maps | Upper semicontinuous set-valued maps | topologies | BOREL SELECTORS | MATHEMATICS | BAIRE CLASS-1 MAPS | SELECTORS | WEAK AND WEAK-ASTERISK TOPOLOGIES | BANACH-SPACES | NAMIOKA | THEOREMS | MAPPINGS | UPPER SEMICONTINUOUS SET-VALUED MAPS

Topological theorems | Mathematical theorems | Mathematical constants | Mathematical functions | Metric spaces | Topology | Banach space | Topological spaces | Continuous functions | Weak and weak | Selectors | Baire class 1 maps | Upper semicontinuous set-valued maps | topologies | BOREL SELECTORS | MATHEMATICS | BAIRE CLASS-1 MAPS | SELECTORS | WEAK AND WEAK-ASTERISK TOPOLOGIES | BANACH-SPACES | NAMIOKA | THEOREMS | MAPPINGS | UPPER SEMICONTINUOUS SET-VALUED MAPS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 8/1993, Volume 118, Issue 4, pp. 1113 - 1115

We give an example of a left amenable discrete semigroup S such that l (S) has weak -closed selfadjoint left translation invariant subalgebras that are weak...

Semigroups | Mathematical functions | Mathematical theorems | Mathematical complements | Subalgebras | Left amenable semigroup | Invariantly complemented subspace | Weak-complemented subspace | Complemented subspace | MATHEMATICS | INVARIANTLY COMPLEMENTED SUBSPACE | MATHEMATICS, APPLIED | COMPLEMENTED SUBSPACE | WEAK-ASTERISK-COMPLEMENTED SUBSPACE | LEFT AMENABLE SEMIGROUP

Semigroups | Mathematical functions | Mathematical theorems | Mathematical complements | Subalgebras | Left amenable semigroup | Invariantly complemented subspace | Weak-complemented subspace | Complemented subspace | MATHEMATICS | INVARIANTLY COMPLEMENTED SUBSPACE | MATHEMATICS, APPLIED | COMPLEMENTED SUBSPACE | WEAK-ASTERISK-COMPLEMENTED SUBSPACE | LEFT AMENABLE SEMIGROUP

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 7/1992, Volume 115, Issue 3, pp. 669 - 676

Let V be an n dimensional subspace of C[ -1, 1]. This paper gives a necessary and sufficient condition for a bounded linear projection P from C[ -1, 1] onto V...

Topological compactness | Sufficient conditions | Polynomials | Mathematical theorems | Vector spaces | Topological vector spaces | Interpolation | Weak | WT measure vector space | Linear projection | topology | MATHEMATICS | MATHEMATICS, APPLIED | LINEAR PROJECTION | INTERPOLATION, WEAK ASTERISK-TOPOLOGY | WT MEASURE VECTOR SPACE

Topological compactness | Sufficient conditions | Polynomials | Mathematical theorems | Vector spaces | Topological vector spaces | Interpolation | Weak | WT measure vector space | Linear projection | topology | MATHEMATICS | MATHEMATICS, APPLIED | LINEAR PROJECTION | INTERPOLATION, WEAK ASTERISK-TOPOLOGY | WT MEASURE VECTOR SPACE

Journal Article

STUDIA MATHEMATICA, ISSN 0039-3223, 1992, Volume 102, Issue 3, pp. 257 - 267

Frechet spaces of strongly, weakly and weak*-continuous Frechet space valued functions are considered. Complete solutions are given to the problems of their...

FRECHET SPACES OF (WEAKLY, WEAK-ASTERISK) CONTINUOUS VECTOR-VALUED FUNCTIONS | SPACES COMPLEMENTED IN DUAL FRECHET SPACES | MATHEMATICS | INJECTIVE FRECHET SPACES | JOSEFSON-NISSENZWEIG THEOREM | COMPLEMENTED COPIES OF CO

FRECHET SPACES OF (WEAKLY, WEAK-ASTERISK) CONTINUOUS VECTOR-VALUED FUNCTIONS | SPACES COMPLEMENTED IN DUAL FRECHET SPACES | MATHEMATICS | INJECTIVE FRECHET SPACES | JOSEFSON-NISSENZWEIG THEOREM | COMPLEMENTED COPIES OF CO

Journal Article

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, ISSN 0362-546X, 02/1993, Volume 20, Issue 4, pp. 405 - 411

Journal Article

Journal of Nonlinear Science, ISSN 0938-8974, 07/1995, Volume 5, Issue 4, pp. 287 - 316

The visual pathway and other brain structures consist of a large number of layers of neurons. At each point of a three-dimensional laminated structure there...

Hebbian learning rule | attractor | Fourier transform | Borel measure | convex functional | weak-topology | autocorrelation | CELLS | MATHEMATICS, APPLIED | FOURIER TRANSFORM | CONVEX FUNCTIONAL | WEAK-ASTERISK TOPOLOGY | AUTOCORRELATION | ATTRACTOR | EMERGENCE | PRINCIPLES | MECHANICS | HEBBIAN LEARNING RULE | ARCHITECTURE | BOREL MEASURE

Hebbian learning rule | attractor | Fourier transform | Borel measure | convex functional | weak-topology | autocorrelation | CELLS | MATHEMATICS, APPLIED | FOURIER TRANSFORM | CONVEX FUNCTIONAL | WEAK-ASTERISK TOPOLOGY | AUTOCORRELATION | ATTRACTOR | EMERGENCE | PRINCIPLES | MECHANICS | HEBBIAN LEARNING RULE | ARCHITECTURE | BOREL MEASURE

Journal Article

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