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mathematics (53) 53
szlenk index (53) 53
banach-spaces (17) 17
mathematics, applied (14) 14
analysis (10) 10
banach space (10) 10
dentability index (9) 9
functional analysis (9) 9
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[ math.math-fa ] mathematics [math]/functional analysis [math.fa] (3) 3
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asymptotically uniformly convex norm (2) 2
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beta (2) 2
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c (2) 2
calculus of variations and optimal control; optimization (2) 2
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dual norm (2) 2
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error analysis (2) 2
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renormings (2) 2
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studies (2) 2
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szlenk indexes (2) 2
unconditional bases (2) 2
uniformly kadec-klee norm (2) 2
universal spaces (2) 2
weakly null sequences (2) 2
46b04 (1) 1
46b04, 54h05 46b15, 46b20, 46b70 (1) 1
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46b80 (1) 1
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47b10 (1) 1
54h05 (1) 1
[math.math-fa]mathematics [math]/functional analysis [math.fa] (1) 1
analytic classes of banach spaces (1) 1
and szlenk index (1) 1
approximation property (1) 1
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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
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
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
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
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
Journal Article
by Raja, M
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
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
Journal Article
Journal of Operator Theory, ISSN 0379-4024, 10/2012, Volume 68, Issue 2, pp. 405 - 442
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
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 04/2011, Volume 260, Issue 8, pp. 2222 - 2246
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
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
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
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
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
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
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
Journal Article
by Raja, M
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
Journal Article
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