Perturbing the spectrum of operator T_n^d(A)

2021/08/27 by Sarajlija, Nikola
#46B25 #46B25 (Secondary) #47A05 #47A08 #47A10 #47A55 (Primary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2108.12153

Abstract

Let T_n^d(A) denote a partial upper triangular operator matrix whose diagonal entries are given and the others unknown. In this article we have aim to find characterizations of (left,right) invertibility of T_n^d(A) in terms of diagonal entries solely, and hence we provide statements which generalize and correct results of Zhang S., Wu Z. (2012). We pose our results without invoking separability condition, thus improving results of Zhang S., Wu Z. (2012), and we give appropriate n-dimensional analogues without assuming separability as well. We recover many perturbation results of Djordjević D. S. (2002), and obtain some results of Du H. K., Pan J. (1994) and Han J. K., Lee H. Y., Lee W. Y. (2000) in the case of the Hilbert space setting.

Related

• Invertibility properties of operator matrices on Hilbert spaces
• Intersections of various spectra of operator matrices
• Upper triangular operator matrices and stability of their various spectra
• Invertible completions of FLI and FRI upper triangular operator matrices
• Perturbation of Browder Spectrum of Upper-triangular Operator Matrices