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The Szlenk power type and tensor products of Banach spaces


Authors: Szymon Draga and Tomasz Kochanek
Journal: Proc. Amer. Math. Soc. 145 (2017), 1685-1698
MSC (2010): Primary 46B20, 46B28
DOI: https://doi.org/10.1090/proc/13339
Published electronically: October 31, 2016
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Abstract: 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 power type as well as summability of the Szlenk index are separably determined, and we extend some of our recent results concerning direct sums.


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Szymon Draga
Affiliation: Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland
Email: szymon.draga@gmail.com

Tomasz Kochanek
Affiliation: Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland – and – Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
Email: tkoch@impan.pl

DOI: https://doi.org/10.1090/proc/13339
Keywords: Szlenk index, Szlenk power type, injective tensor product, direct sum
Received by editor(s): April 12, 2016
Received by editor(s) in revised form: June 9, 2016, and June 17, 2016
Published electronically: October 31, 2016
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2016 American Mathematical Society