Bulletin of the Korean Mathematical Society (대한수학회보)

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A NOTE ON THE PROPERTIES OF PSEUDO-WEIGHTED BROWDER SPECTRUM

  • Received : 2021.12.28
  • Accepted : 2022.06.15
  • Published : 2023.01.31
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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 α-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

Acknowledgement

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

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