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November 2019 Wigner’s theorem on the Tsirelson space T
Yuanxia Li, Dongni Tan
Ann. Funct. Anal. 10(4): 515-524 (November 2019). DOI: 10.1215/20088752-2019-0010

Abstract

We say that a map f:XY between two real normed spaces is a phase-isometry if {f(x)+f(y),f(x)f(y)}={x+y,xy} holds for all x,yX. Two maps f,g:XY are called phase-equivalent if there is a phase function ε:X{1,1} such that εf=g. By studying the properties of surjective phase-isometries on the Tsirelson space T, we show that such maps are phase-equivalent to linear isometries. This gives a real version of Wigner’s theorem for the Tsirelson space.

Citation

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Yuanxia Li. Dongni Tan. "Wigner’s theorem on the Tsirelson space T." Ann. Funct. Anal. 10 (4) 515 - 524, November 2019. https://doi.org/10.1215/20088752-2019-0010

Information

Received: 16 September 2018; Accepted: 4 February 2019; Published: November 2019
First available in Project Euclid: 29 October 2019

zbMATH: 07126069
MathSciNet: MR4026365
Digital Object Identifier: 10.1215/20088752-2019-0010

Subjects:
Primary: 46B04
Secondary: 46B20

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 4 • November 2019
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