Turkish Journal of Analysis and Number Theory
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Turkish Journal of Analysis and Number Theory. 2022, 10(1), 21-26
DOI: 10.12691/tjant-10-1-5
Open AccessArticle

Some Spectral Characteristic Numbers of Direct Sum of Operators

Zameddin I. Ismailov1, and Pembe Ipek Al1

1Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Turkey

Pub. Date: December 30, 2022

Cite this paper:
Zameddin I. Ismailov and Pembe Ipek Al. Some Spectral Characteristic Numbers of Direct Sum of Operators. Turkish Journal of Analysis and Number Theory. 2022; 10(1):21-26. doi: 10.12691/tjant-10-1-5

Abstract

In the present study, firstly, some algebraic inequalities are proved, which will be used later. By making use of these relations, some evaluations are found related the gaps between norm and numerical radius, spectral radius and Crawford number for diagonal block operator matrices on the infinite direct sum of Hilbert spaces. Later on, the gaps between some spectral characteristic numbers (operator norm, lower and upper bounds of spectrum set and numerical radius) of the infinite direct sum of Hilbert space operators relatively to the same spectral characteristics of the coordinate operators are investigated. Then, the obtained results are supported by applications. The open problem posed by Demuth in 2015 and the works of Kittaneh and his researcher group in this area had an important effect on the formation of the subject discussed in this study.

Keywords:
operator norm spectral radius numerical radius CRAWFORD number

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