STUDIA MATHEMATICA, ISSN 0039-3223, 2017, Volume 236, Issue 3, pp. 201 - 244

We discuss pruning and coloring lemmas on regular families. We discuss several applications of these lemmas to computing the Szlenk index of certain w...

universality | MATHEMATICS | THEOREM | embedding in spaces with finite dimensional decompositions | SUBSETS | Ramsey theory | Szlenk index | REFLEXIVE BANACH-SPACES | L-INDEX

universality | MATHEMATICS | THEOREM | embedding in spaces with finite dimensional decompositions | SUBSETS | Ramsey theory | Szlenk index | REFLEXIVE BANACH-SPACES | L-INDEX

Journal Article

STUDIA MATHEMATICA, ISSN 0039-3223, 2019, Volume 248, Issue 2, pp. 109 - 127

In a previous work, the first named author described the set P of all values of the Szlenk indices of separable Banach spaces...

MATHEMATICS | ASYMPTOTICALLY UNIFORMLY SMOOTH | Szlenk index | PROPERTY

MATHEMATICS | ASYMPTOTICALLY UNIFORMLY SMOOTH | Szlenk index | PROPERTY

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 04/2017, Volume 272, Issue 8, pp. 3375 - 3409

Given any Banach space X and any weak⁎-compact subset K of X⁎, we compute the Szlenk index of the weak...

Tensor products | Banach spaces | Szlenk index | Ordinal indices | MATHEMATICS | BANACH-SPACES | ASPLUND SPACES

Tensor products | Banach spaces | Szlenk index | Ordinal indices | MATHEMATICS | BANACH-SPACES | ASPLUND SPACES

Journal Article

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

.... We apply our results to the Kuratowski measure of non-compactness and to the study of the Szlenk index of a Banach space...

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

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

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...

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 08/2016, Volume 271, Issue 3, pp. 642 - 671

We prove that the c0-sum of separable Banach spaces with uniformly summable Szlenk index has summable Szlenk index, whereas this result is no longer valid for more general direct sums...

Asymptotic structure | Tsirelson space | Szlenk index | MATHEMATICS | BANACH-SPACES

Asymptotic structure | Tsirelson space | Szlenk index | MATHEMATICS | BANACH-SPACES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2012, Volume 391, Issue 2, pp. 496 - 509

The Szlenk index has found many applications in the isomorphic theory of Banach spaces...

spaces | Szlenk index | Uniformly Kadec-Klee norm

spaces | Szlenk index | Uniformly Kadec-Klee norm

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 353, Issue 1, pp. 239 - 243

We compute the weak ∗-dentability index of the spaces C ( K ) where K is a countable compact space. Namely Dz ( C ( [ 0 , ω ω α ] ) ) = ω 1 + α + 1 , whenever 0 ⩽ α < ω 1...

Szlenk index | Dentability index | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | Mathematics - Functional Analysis

Szlenk index | Dentability index | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | Mathematics - Functional Analysis

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...

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

Positivity, ISSN 1385-1292, 12/2017, Volume 21, Issue 4, pp. 1507 - 1525

.../10.1007/s11117-017-0482-0 We prove the optimal estimate between the Szlenk and w.sup.* w ? -dentability indices of an arbitrary...

Asplund space | Szlenk index | Dentability index | Banach space | Game theory | Banach spaces

Asplund space | Szlenk index | Dentability index | Banach space | Game theory | Banach spaces

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 04/2011, Volume 260, Issue 8, pp. 2222 - 2246

For α an ordinal and 1

Asplund operators | Banach spaces | Direct sums | Szlenk index | MATHEMATICS | UNIVERSAL | BANACH-SPACES | Mathematics - Functional Analysis

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2020, Volume 489, Issue 1, p. 124167

We prove that for any non-zero, countable ordinal ξ which is not additively indecomposable, the property of having Szlenk index not exceeding ωξ...

Three space property | Szlenk index | MATHEMATICS | MATHEMATICS, APPLIED | ASYMPTOTICALLY UNIFORMLY SMOOTH | BANACH-SPACES

Three space property | Szlenk index | MATHEMATICS | MATHEMATICS, APPLIED | ASYMPTOTICALLY UNIFORMLY SMOOTH | BANACH-SPACES

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...

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

Studia Mathematica, ISSN 0039-3223, 2013, Volume 216, Issue 2, pp. 149 - 178

For each ordinal alpha < omega(1), we prove the existence of a Banach space with a basis and Szlenk index omega(alpha+1...

Schreier spaces | Embedding in spaces with finite-dimensional decompositions | Szlenk index | Universality | universality | MATHEMATICS | UNIVERSAL BASES | embedding in spaces with finite-dimensional decompositions | QUOTIENTS

Schreier spaces | Embedding in spaces with finite-dimensional decompositions | Szlenk index | Universality | universality | MATHEMATICS | UNIVERSAL BASES | embedding in spaces with finite-dimensional decompositions | QUOTIENTS

Journal Article

Studia Mathematica, ISSN 0039-3223, 2007, Volume 183, Issue 1, pp. 63 - 97

For a countable ordinal a we denote by C-alpha the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by alpha...

Embedding into FDDs | Universal space | Szlenk index | Analytic classes | Effros-Borel structure | MATHEMATICS | analytic classes | UNIVERSAL | universal space | TSIRELSON SPACE | embedding into FDDs | L-INDEX

Embedding into FDDs | Universal space | Szlenk index | Analytic classes | Effros-Borel structure | MATHEMATICS | analytic classes | UNIVERSAL | universal space | TSIRELSON SPACE | embedding into FDDs | L-INDEX

Journal Article

Fundamenta Mathematicae, ISSN 0016-2736, 2009, Volume 205, Issue 2, pp. 161 - 177

For every alpha < omega(1) we establish the existence of a separable Banach space whose Szlenk index is omega(alpha omega+1...

Effros-borel structure | Embedding into FFDs | Universal space | Szlenk index | Analytic classes | MATHEMATICS | analytic classes | universal space | UNCONDITIONAL BASES | SUBSPACES | QUOTIENTS | embedding into FDDs | Effros-Borel structure

Effros-borel structure | Embedding into FFDs | Universal space | Szlenk index | Analytic classes | MATHEMATICS | analytic classes | universal space | UNCONDITIONAL BASES | SUBSPACES | QUOTIENTS | embedding into FDDs | Effros-Borel structure

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2019, Volume 479, Issue 1, pp. 1324 - 1354

We give necessary and sufficient conditions for an operator A:X→Y on a Banach space having a shrinking FDD to factor through a Banach space Z such that the Szlenk index of Z is equal to the Szlenk index...

Asplund operators | Operator ideals | Szlenk index | Factorization | MATHEMATICS | COMPACT | MATHEMATICS, APPLIED | SET | THEOREM | BANACH-SPACES | PROPERTY

Asplund operators | Operator ideals | Szlenk index | Factorization | MATHEMATICS | COMPACT | MATHEMATICS, APPLIED | SET | THEOREM | BANACH-SPACES | PROPERTY

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 07/2020, Volume 278, Issue 12, p. 108470

... of countably branching trees into reflexive Banach spaces whose Szlenk index and Szlenk index from the dual are both equal to the first infinite ordinal ω...

Countably branching trees | Equi-Lipschitz embeddability | Asymptotic uniform properties | Szlenk index | MATHEMATICS

Countably branching trees | Equi-Lipschitz embeddability | Asymptotic uniform properties | Szlenk index | MATHEMATICS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 12/2007, Volume 253, Issue 1, pp. 273 - 286

We study the relationships between the ordinal indices of set derivations associated to several measures of non-compactness...

Renorming | Dentability index | Measures of non-compactness | Szlenk index | MATHEMATICS | renorming | dentability index | measures of non-compactness | SPACES

Renorming | Dentability index | Measures of non-compactness | Szlenk index | MATHEMATICS | renorming | dentability index | measures of non-compactness | SPACES

Journal Article

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