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Keywords:
local spectrum; local spectral radius; linear preservers
Summary:
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.
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