Essentially spectrally bounded linear maps

Bendaoud, M.; Bourhim, A.

doi:10.1090/S0002-9939-09-09815-3

Essentially spectrally bounded linear maps
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by M. Bendaoud and A. Bourhim PDF

Proc. Amer. Math. Soc. 137 (2009), 3329-3334 Request permission

Abstract:

Let ${\mathcal L}({\mathcal {H}})$ be the algebra of all bounded linear operators on an infinite dimensional complex Hilbert space ${\mathcal {H}}$. We characterize essentially spectrally bounded linear maps from ${\mathcal L}( {\mathcal {H}})$ onto ${\mathcal L}({\mathcal {H}})$ itself. As a consequence, we characterize linear maps from ${\mathcal L}( {\mathcal {H}})$ onto ${\mathcal L}({\mathcal {H}})$ itself that compress different essential spectral sets such as the the essential spectrum, the (left, right) essential spectrum, and the semi-Fredholm spectrum.

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