## Involve: A Journal of Mathematics

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

### Time stopping for Tsirelson's norm

#### Abstract

Tsirelson’s norm $∥⋅∥T$ on $c00$ is defined as the limit of an increasing sequence of norms $(∥⋅∥n)n=1∞$. For each $n∈ℕ$ let $j(n)$ be the smallest integer satisfying $∥x∥j(n)=∥x∥T$ for all $x$ with $maxsuppx=n$. We show that $j(n)$ is $O(n1∕2)$. 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
Revised: 21 July 2017
Accepted: 14 August 2017
First available in Project Euclid: 12 April 2018

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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