Bulletin of the
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Bull. Korean Math. Soc. 2023; 60(1): 123-135

Online first article January 25, 2023      Printed January 31, 2023

https://doi.org/10.4134/BKMS.b210931

Copyright © The Korean Mathematical Society.

A note on the properties of pseudo-weighted Browder spectrum

Preeti Dharmarha, Sarita Kumari

Hansraj College; Department of Mathematics

Abstract

The goal of this article is to introduce the concept of pseudo-weighted Browder spectrum when the underlying Hilbert space is not necessarily separable. To attain this goal, the notion of $\alpha$-pseudo-Browder operator has been introduced. The properties and the relation of the weighted spectrum, pseudo-weighted spectrum, weighted Browder spectrum, and pseudo-weighted Browder spectrum have been investigated by extending analogous properties of their corresponding essential pseudo-spectrum and essential pseudo-weighted spectrum. The weighted spectrum, pseudo-weighted spectrum, weighted Browder, and pseudo-weighted Browder spectrum of the sum of two bounded linear operators have been characterized in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces. This exploration ends with a characterization of the pseudo-weighted Browder spectrum of the sum of two bounded linear operators defined over the arbitrary Hilbert spaces under certain conditions.

Keywords: Weighted Weyl spectrum, weighted Browder spectrum, pseudo-weighted Browder spectrum

MSC numbers: Primary 47A53

Supported by: The research of the second author is supported by CSIR, India with reference no.: 09/045(1728)/2019-EMR-I.

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