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On the geometry of projective tensor products

Giladi, Ohad; Prochno, Joscha; Schütt, Carsten; Tomczak-Jaegermann, Nicole; Werner, Elisabeth

Authors

Ohad Giladi

Joscha Prochno

Carsten Schütt

Nicole Tomczak-Jaegermann

Elisabeth Werner



Abstract

© 2017 Elsevier Inc. In this work, we study the volume ratio of the projective tensor products ℓpn⊗πℓqn⊗πℓrnwith 1≤p≤q≤r≤∞. We obtain asymptotic formulas that are sharp in almost all cases. As a consequence of our estimates, these spaces allow for a nearly Euclidean decomposition of Kašin type whenever 1≤p≤q≤r≤2 or 1≤p≤2≤r≤∞ and q=2. Also, from the Bourgain–Milman bound on the volume ratio of Banach spaces in terms of their cotype 2 constant, we obtain information on the cotype of these 3-fold projective tensor products. Our results naturally generalize to k-fold products ℓp1n⊗π…⊗πℓpknwith k∈N and 1≤p1≤…≤pk≤∞.

Citation

Giladi, O., Prochno, J., Schütt, C., Tomczak-Jaegermann, N., & Werner, E. (2017). On the geometry of projective tensor products. Journal of functional analysis, 273(2), 471-495. https://doi.org/10.1016/j.jfa.2017.03.019

Journal Article Type Article
Acceptance Date Mar 31, 2017
Online Publication Date Apr 10, 2017
Publication Date Jul 15, 2017
Deposit Date Jun 29, 2018
Publicly Available Date Oct 27, 2022
Journal Journal of Functional Analysis
Print ISSN 0022-1236
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 273
Issue 2
Pages 471-495
DOI https://doi.org/10.1016/j.jfa.2017.03.019
Keywords Tensor product; Volume ratio; Cotype
Public URL https://hull-repository.worktribe.com/output/900231
Publisher URL https://www.sciencedirect.com/science/article/pii/S0022123617301489
Additional Information This article is maintained by: Elsevier; Article Title: On the geometry of projective tensor products; Journal Title: Journal of Functional Analysis; CrossRef DOI link to publisher maintained version: http://dx.doi.org/10.1016/j.jfa.2017.03.019; Content Type: article; Copyright: © 2017 Elsevier Inc. All rights reserved.
Contract Date Jun 29, 2018