Linear Essential Spectrum Compressors
Keywords:
Fredholm elements, essential spectrum, Weyl spectrum, essential spectral radius, linear preservers.Abstract
Let $A$ be a unital $C^{*}$-algebra of real rank zero and $B$ be a
unital semisimple complex Banach algebra. We characterize linear
maps from $A$ onto $B$ that compress different essential spectral
sets such as the (left, right) essential spectrum, the
semi-Fredholm spectrum, and the Weyl spectrum. Essentially
spectrally bounded linear mapping from $A$ onto $B$ are also
characterized.
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