Abstract
This paper presents: 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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