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2014 Linear maps between operator algebras preserving certain spectral functions
Xiaohong Cao, Shizhao Chen
Banach J. Math. Anal. 8(1): 39-46 (2014). DOI: 10.15352/bjma/1381782085

Abstract

Let $H$ be an infinite dimensional complex Hilbert space and let $\phi$ be a surjective linear map on $B(H)$ with $\phi(I)-I\in{\mathcal{K}}(H)$, where $\mathcal{K}(H)$ denotes the closed ideal of all compact operators on $H$. If $\phi$ preserves the set of upper semi-Weyl operators and the set of all normal eigenvalues in both directions, then $\phi$ is an automorphism of the algebra $B(H)$. Also the relation between the linear maps preserving the set of upper semi-Weyl operators and the linear maps preserving the set of left invertible operators is considered.

Citation

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Xiaohong Cao. Shizhao Chen. "Linear maps between operator algebras preserving certain spectral functions." Banach J. Math. Anal. 8 (1) 39 - 46, 2014. https://doi.org/10.15352/bjma/1381782085

Information

Published: 2014
First available in Project Euclid: 14 October 2013

zbMATH: 1290.47038
MathSciNet: MR3161680
Digital Object Identifier: 10.15352/bjma/1381782085

Subjects:
Primary: 47B48
Secondary: 46H05, 47A10

Rights: Copyright © 2014 Tusi Mathematical Research Group

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Vol.8 • No. 1 • 2014
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