Gustafson, Jeribi, Weidmann and Wolf essential spectra and generator properties for one-sided coupled operator matrices
Lei Zhao, Jing Xu, Junjie Huang · Linear and Multilinear Algebra · 2024
This paper is concerned with the closedness (closability), essential spectra and generator properties for a one-sided coupled operator matrix A0 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 A0 are collected, including perturbations, closedness and spectra. Utilizing these results, we present a necessary and sufficient condition for A0 to be closed (closable), and the essential spectra as well as generator properties of A0 are further described.