Involve: A Journal of Mathematics

  • Involve
  • Volume 11, Number 5 (2018), 857-866.

Time stopping for Tsirelson's norm

Kevin Beanland, Noah Duncan, and Michael Holt

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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.

Article information

Involve, Volume 11, Number 5 (2018), 857-866.

Received: 18 April 2017
Revised: 21 July 2017
Accepted: 14 August 2017
First available in Project Euclid: 12 April 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B03: Isomorphic theory (including renorming) of Banach spaces

Tsirelson's space Banach space


Beanland, Kevin; Duncan, Noah; Holt, Michael. Time stopping for Tsirelson's norm. Involve 11 (2018), no. 5, 857--866. doi:10.2140/involve.2018.11.857.

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