## Banach Journal of Mathematical Analysis

### Linear maps between operator algebras preserving certain spectral functions

#### 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.

#### Article information

Source
Banach J. Math. Anal., Volume 8, Number 1 (2014), 39-46.

Dates
First available in Project Euclid: 14 October 2013

https://projecteuclid.org/euclid.bjma/1381782085

Digital Object Identifier
doi:10.15352/bjma/1381782085

Mathematical Reviews number (MathSciNet)
MR3161680

Zentralblatt MATH identifier
1290.47038

#### Citation

Cao, Xiaohong; Chen, Shizhao. Linear maps between operator algebras preserving certain spectral functions. Banach J. Math. Anal. 8 (2014), no. 1, 39--46. doi:10.15352/bjma/1381782085. https://projecteuclid.org/euclid.bjma/1381782085

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