Vol. 11, No. 5, 2018

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Time stopping for Tsirelson's norm

Kevin Beanland, Noah Duncan and Michael Holt

Vol. 11 (2018), No. 5, 857–866
Abstract

Tsirelson’s norm T on c00 is defined as the limit of an increasing sequence of norms (n)n=1. For each n let j(n) be the smallest integer satisfying xj(n) = xT for all x with maxsuppx = n. We show that j(n) is O(n12). This is an improvement of the upper bound of O(n) given by P. Casazza and T. Shura in their 1989 monograph on Tsirelson’s space.

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Keywords
Tsirelson's space, Banach space
Mathematical Subject Classification 2010
Primary: 46B03
Milestones
Received: 18 April 2017
Revised: 21 July 2017
Accepted: 14 August 2017
Published: 2 April 2018

Communicated by Stephan Garcia
Authors
Kevin Beanland
Department of Mathematics
Washington and Lee University
Lexington, VA
United States
Noah Duncan
Department of Mathematics
Washington and Lee University
Lexington, VA
United States
Michael Holt
Department of Mathematics
Washington and Lee University
Lexington, VA
United States