Determinant Spectrum of Diagonal Block Matrix

Elif OTKUN CEVIK\(^{a,*}\), Zameddin I. ISMAILOV\(^b\)
\(^a\)Department of Mathematics, Avrasya University, Trabzon, Turkey.
\(^b\)Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey.
Correspondence should be addressed to: Elif OTKUN EVIK at elifotkuncevik@gmail.com

Copyright © 2021 Elif OTKUN CEVIK, Zameddin I. ISMAILOV. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 5 March 2020; Accepted: 5 November 2020; Published Online: 18 May 2021.

Abstract

It is known that in mathematical literature one of important questions of spectral theory of operators is to describe spectrum of diagonal block matrices in the direct sum of Banach spaces with the spectrums of their coordinate operators. This problem has been investigated in works [1] and [2]. Also for the singular numbers similar investigation has been made in [3]. In this paper the analogous question is researched. Namely, the relationships between \(\epsilon\)-determinat spectrums of the diagonal block matrices and their block matrices are investigated. Later on, some applications are given.

Keywords:

Eigenvalues, Spectrum, Determinant, Diagonal Block Matrix.