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.References
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Additional Information
- M. Bendaoud
- Affiliation: Département de Mathématiques, Université Moulay Ismail, Meknès, Morocco
- Email: bendaoudmohamed@gmail.com
- A. Bourhim
- Affiliation: Département de Mathématiques et de Statistique, Université Laval, Québec G1K 7P4, Canada
- Address at time of publication: Department of Mathematics, Syracuse University, 215 Carnegie Building, Syracuse, New York 13244
- MR Author ID: 685154
- Email: bourhim@mat.ulaval.ca, abourhim@syr.edu
- Received by editor(s): June 23, 2008
- Published electronically: June 5, 2009
- Additional Notes: The second author was supported by an adjunct professorship at Laval University
- Communicated by: Nigel J. Kalton
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 3329-3334
- MSC (2000): Primary 47B49; Secondary 47A10, 47D25
- DOI: https://doi.org/10.1090/S0002-9939-09-09815-3
- MathSciNet review: 2515402