Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589586 | Journal of Functional Analysis | 2016 | 30 Pages |
Abstract
We prove that the c0c0-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of separable Banach spaces with uniformly summable Szlenk index has summable Szlenk index, whereas this result is no longer valid for more general direct sums. We also give a formula for the Szlenk power type of the EE-direct sum of separable spaces provided that EE has a shrinking unconditional basis whose dual basis yields an asymptotic ℓpℓp structure in E⁎E⁎. As a corollary, we show that the Tsirelson direct sum of infinitely many copies of c0c0 has power type 1 but non-summable Szlenk index.
Keywords
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Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Szymon Draga, Tomasz Kochanek,