Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Essentially spectrally bounded linear maps

Author(s): M. Bendaoud; A. Bourhim
Journal: Proc. Amer. Math. Soc. 137 (2009), 3329-3334.
MSC (2000): Primary 47B49; Secondary 47A10, 47D25
Posted: June 5, 2009
MathSciNet review: 2515402
Retrieve article in: PDF

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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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