Abstract
This paper is concerned with the closedness (closability), essential spectra and generator properties for a one-sided coupled operator matrix A 0 acting in a product of Banach spaces X and Y. By combining the Browder Resolvent with the Schur factorization, some basic properties related to the operator entries of A 0 are collected, including perturbations, closedness and spectra. Utilizing these results, we present a necessary and sufficient condition for A 0 to be closed (closable), and the essential spectra as well as generator properties of A 0 are further described.
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