Taiwanese Journal of Mathematics

LINEAR ORTHOGONALITY PRESERVERS OF STANDARD OPERATOR ALGEBRAS

Chung-Wen Tsai and Ngai-Ching Wong

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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.

Article information

Source
Taiwanese J. Math., Volume 14, Number 3B (2010), 1047-1053.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405904

Digital Object Identifier
doi:10.11650/twjm/1500405904

Mathematical Reviews number (MathSciNet)
MR2674595

Zentralblatt MATH identifier
1227.47024

Subjects
Primary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25] 46L05: General theory of $C^*$-algebras

Keywords
linear orthogonality preservers standard operator algebras autocontinuity

Citation

Tsai, Chung-Wen; Wong, Ngai-Ching. LINEAR ORTHOGONALITY PRESERVERS OF STANDARD OPERATOR ALGEBRAS. Taiwanese J. Math. 14 (2010), no. 3B, 1047--1053. doi:10.11650/twjm/1500405904. https://projecteuclid.org/euclid.twjm/1500405904


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References

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