(untitled) (European Journal of Pure and Applied Mathematics, 2017)
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.