Geodesic
Locally spectrally bounded linear maps
Mathematica Bohemica, Tome 136 (2011) no. 1, pp. 81-89
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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.
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.
DOI : 10.21136/MB.2011.141452
Classification : 47A10, 47A53, 47B49
Keywords: local spectrum; local spectral radius; linear preservers 
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Bendaoud, M.; Sarih, M. Locally spectrally bounded linear maps. Mathematica Bohemica, Tome 136 (2011) no. 1, pp. 81-89. doi: 10.21136/MB.2011.141452

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