On the geometry of projective tensor products

Title: On the geometry of projective tensor products
Creator: Giladi, Ohad; Prochno, Joscha; Schütt, Carsten; Tomczak-Jaegermann, Nicole; Werner, Elizabeth
Relation: Funding BodyARC.Grant NumberDP160101537 http://purl.org/au-research/grants/arc/DP160101537
Relation: Journal of Functional Analysis Vol. 273, Issue 2, p. 471-495
Publisher Link: http://dx.doi.org/10.1016/j.jfa.2017.03.019
Publisher: Academic Press
Resource Type: journal article
Date: 2017
Description: In this work, we study the volume ratio of the projective tensor products [formula could not be replicated] with 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 [formula could not be replicated] with k ∈ ℕ and 1 ≤ p₁ ≤ ... ≤ p_k ≤ ∞ .
Subject: tensor product; volume ratio; cotype; asymptotic formulas
Identifier: http://hdl.handle.net/1959.13/1400877
Identifier: uon:34825
Identifier: ISSN:0022-1236
Language: eng
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