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M. Bendaoud, Universite Moulay Ismail, Ecole Nationale Superieure d'Arts et Metiers, Departement de Mathematiques et Informatique, B.P. 4024 Beni Mhamed, Marjane II, Meknes, Maroc, e-mail: bendaoud@fs-umi.ac.ma; M. Sarih, University Moulay Ismail, Faculte des Sciences, Departement de Mathematiques, BP 11201, Zitoune, Meknes, Maroc, e-mail: sarih@fs-umi.ac.ma
Abstract: Let ${\mathcal L}({\mathcal H})$ be the algebra of all bounded linear operators on a complex Hilbert space ${\mathcal H}$. We characterize locally spectrally bounded linear maps from ${\mathcal L}({\mathcal H})$ onto itself. As a consequence, we describe linear maps from ${\mathcal L}({\mathcal H})$ onto itself that compress the local spectrum.
Keywords: local spectrum, local spectral radius, linear preservers
Classification (MSC 2000): 47B49, 47A10, 47A53
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