$S$-spectra and $S$-essential pseudospectra of the diagonal block operator matrices

Abstract

In this article, the relationships between the $S$-spectra, the $ S$-spectral radius, the $ \epsilon$-$S$-essential pseudospectra, and the $ \epsilon$-$S$-essential pseudospectral radius of the diagonal block operator matrices in the direct sum of Banach spaces and their block coordinate operators are studied. Then, the results are supported by applications.