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.
Preeti Dharmarha, Sarita Kumari
Hansraj College; Department of Mathematics
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.
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd