Taiwanese Journal of Mathematics

MAPS PRESERVING LIE PRODUCT ON B(X)

Xiuping Xiuping and Fangyan Lu

Full-text: Open access

Abstract

Banach spaces. Let $\phi$ be a bijection from $B(X)$ onto $B(Y)$ satisfying ${\phi}([A,B])=[\phi(A),\phi(B)]$ for all $A, B\in B(X)$. Then $\phi=\psi+\tau$, where $\psi$ is a ring isomorphism or a negative of a ring anti-isomorphism from $B(X)$ onto $B(Y)$, and $\tau$ is a map from $B(X)$ into $\Bbb CI$ satisfying $\tau([A,B])=0$ for all $A, B\in B(X)$.

Article information

Source
Taiwanese J. Math., Volume 12, Number 3 (2008), 793-806.

Dates
First available in Project Euclid: 21 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500602436

Digital Object Identifier
doi:10.11650/twjm/1500602436

Mathematical Reviews number (MathSciNet)
MR2417148

Zentralblatt MATH identifier
1159.47020

Subjects
Primary: 47B49: Transformers, preservers (operators on spaces of operators) 47L10: Algebras of operators on Banach spaces and other topological linear spaces

Keywords
Lie product Banach spaces ring isomorphism

Citation

Xiuping, Xiuping; Lu, Fangyan. MAPS PRESERVING LIE PRODUCT ON B(X). Taiwanese J. Math. 12 (2008), no. 3, 793--806. doi:10.11650/twjm/1500602436. https://projecteuclid.org/euclid.twjm/1500602436


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