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2010 LINEAR ORTHOGONALITY PRESERVERS OF STANDARD OPERATOR ALGEBRAS
Chung-Wen Tsai, Ngai-Ching Wong
Taiwanese J. Math. 14(3B): 1047-1053 (2010). DOI: 10.11650/twjm/1500405904

Abstract

In 2003, Araujo and Jarosz showed that every bijective linear map $\theta: A \to B$ between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both $A,B$ are unital standard algebras on Hilbert spaces and $\theta$ preserves range or domain orthogonality. In particular, such maps are automatically bounded. In this paper, we will study linear orthogonality preservers in a unified way. We will show that every surjective linear map between standard operator algebras preserving range/domain orthogonality carries a standard form, and is thus automatically bounded.

Citation

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Chung-Wen Tsai. Ngai-Ching Wong. "LINEAR ORTHOGONALITY PRESERVERS OF STANDARD OPERATOR ALGEBRAS." Taiwanese J. Math. 14 (3B) 1047 - 1053, 2010. https://doi.org/10.11650/twjm/1500405904

Information

Published: 2010
First available in Project Euclid: 18 July 2017

zbMATH: 1227.47024
MathSciNet: MR2674595
Digital Object Identifier: 10.11650/twjm/1500405904

Subjects:
Primary: 46J10, 46L05

Rights: Copyright © 2010 The Mathematical Society of the Republic of China

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Vol.14 • No. 3B • 2010
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