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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.involve/1523498548

Digital Object Identifier
doi:10.2140/involve.2018.11.857

Mathematical Reviews number (MathSciNet)
MR3784031

Zentralblatt MATH identifier
06866588

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

Keywords
Tsirelson's space Banach space

Citation

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. https://projecteuclid.org/euclid.involve/1523498548


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References

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