Operator ideals and three-space properties of asymptotic ideal seminorms
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- by Ryan M. Causey, Szymon Draga and Tomasz Kochanek PDF
- Trans. Amer. Math. Soc. 371 (2019), 8173-8215 Request permission
Abstract:
We introduce asymptotic analogues of the Rademacher and martingale type and cotype of Banach spaces and operators acting on them. Some classical local theory results related, for example, to the “automatic-type" phenomenon, the type-cotype duality, or the Maurey–Pisier theorem are extended to the asymptotic setting. We also investigate operator ideals corresponding to the asymptotic subtype/subcotype. As an application of this theory, we provide a sharp version of a result of Brooker and Lancien by showing that any twisted sum of Banach spaces with Szlenk power types $p$ and $q$ has Szlenk power type $\max \{p,q\}$.References
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Additional Information
- Ryan M. Causey
- Affiliation: Department of Mathematics, Miami University, Oxford, Ohio 45056
- MR Author ID: 923618
- Email: causeyrm@miamioh.edu
- Szymon Draga
- Affiliation: Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Prague 1, Czech Republic
- MR Author ID: 1024172
- 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
- MR Author ID: 811694
- Email: tkoch@impan.pl
- Received by editor(s): January 6, 2018
- Received by editor(s) in revised form: November 11, 2018, and November 16, 2018
- Published electronically: January 16, 2019
- Additional Notes: Research of the second author was supported by GAČR project 16-34860L and RVO: 67985840.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 8173-8215
- MSC (2010): Primary 46B06, 46B20, 46B28; Secondary 46B09
- DOI: https://doi.org/10.1090/tran/7759
- MathSciNet review: 3955545