Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772330 | Journal of Functional Analysis | 2017 | 25 Pages |
Abstract
In this work, we study the volume ratio of the projective tensor products âpnâÏâqnâÏârn with 1â¤pâ¤qâ¤râ¤â. 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 KaÅ¡in type whenever 1â¤pâ¤qâ¤râ¤2 or 1â¤pâ¤2â¤râ¤â 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 âp1nâÏâ¦âÏâpkn with kâN and 1â¤p1â¤â¦â¤pkâ¤â.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ohad Giladi, Joscha Prochno, Carsten Schütt, Nicole Tomczak-Jaegermann, Elisabeth Werner,