# Bulletin of theKorean Mathematical SocietyBKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

## Article

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Bull. Korean Math. Soc. 2022; 59(1): 1-13

Published online January 31, 2022 https://doi.org/10.4134/BKMS.b200328

## On weighted Browder spectrum

Preeti Dharmarha, Sarita Kumari

University of Delhi; University of Delhi

### Abstract

The main aim of the article is to introduce new generalizations of Fredholm and Browder classes of spectra when the underlying Hilbert space is not necessarily separable and study their properties. To achieve the goal the notions of $\alpha$-Browder operators, $\alpha$-B-Fredholm operators, $\alpha$-B-Browder operators and $\alpha$-Drazin invertibility have been introduced. The relation of these classes of operators with their corresponding weighted spectra has been investigated. An equivalence of $\alpha$-Drazin invertible operators with $\alpha$-Browder operators and $\alpha$-B-Browder operators has also been established. The weighted Browder spectrum of the sum of two bounded linear operators has been characterised in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces.

Keywords: Weighted Browder spectrum, weighted B-Browder spectrum, $\alpha$-Drazin invertibility

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.