Bull. Korean Math. Soc. 2022; 59(1): 1-13
Online first article January 11, 2022 Printed January 31, 2022
https://doi.org/10.4134/BKMS.b200328
Copyright © The Korean Mathematical Society.
Preeti Dharmarha, Sarita Kumari
University of Delhi; University of Delhi
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.
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