2021/08/27 by Nikola Sarajlija, Sarajlija, Nikola
Computer Science · Mathematics · #46B26 (Secondary) #47A10 #47A53 (Primary) #47A55 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2108.12310
openalex publication_date 2021/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with general n× n upper triangular operator matrices with given diagonal entries. We characterize perturbations of the left (right) essential spectrum, the essential spectrum, as well as the left (right) the Weyl spectrum of such operators, thus generalizing and improving some results of \citeCAO, \citeCAO2, \citeSUNTHEORY, \citeSUN, \citeLIandDU, \citeZHANG from n=2 to case of n≥2. We show that related results hold in arbitrary Banach spaces without assuming separability, thus extending and improving recent results from \citeWU, \citeWU2. For the lack of adjointness and orthogonality in Banach spaces, we use an adequate alternative: the concept of inner generalized inverse.