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- W2044666512 abstract "Let $H$ be an infinite-dimensional separable complex Hilbert space and $mathcal {B}(H)$ the algebra of all bounded linear operators on $H$. In this paper we characterize surjective linear maps $phi : Fmathcal {B}(H)to mathcal {B}(H)$ preserving the set of Fredholm operators in both directions. As an application we prove that $phi$ preserves the essential spectrum if and only if the ideal of all compact operators is invariant under $phi$ and the induced linear map $varphi$ on the Calkin algebra is either an automorphism, or an anti-automorphism. Moreover, we have, either $ind(phi (T)) = ind(T)$ or $ind(phi (T)) = - ind(T)$ for every Fredholm operator $T$." @default.
- W2044666512 created "2016-06-24" @default.
- W2044666512 creator A5011686981 @default.
- W2044666512 date "2007-11-01" @default.
- W2044666512 modified "2023-10-16" @default.
- W2044666512 title "Linear maps preserving the set of Fredholm operators" @default.
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- W2044666512 doi "https://doi.org/10.1090/s0002-9939-07-08874-0" @default.
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