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
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
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