Generalized Browder's and Weyl's theorems for left and right   multiplication operators

Enrico Boasso; B. P. Duggal; I. H. Jeon

arXiv:1307.5020·math.FA·July 19, 2013

Generalized Browder's and Weyl's theorems for left and right multiplication operators

Enrico Boasso, B. P. Duggal, I. H. Jeon

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TL;DR

This paper investigates the extension of Browder's and Weyl's theorems to multiplication operators and elementary operators, broadening the understanding of spectral properties in operator theory.

Contribution

It introduces generalized versions of Browder's and Weyl's theorems specifically for multiplication and elementary operators, which were not previously established.

Findings

01

Extended Browder's and Weyl's theorems to multiplication operators

02

Characterized spectral properties of elementary operators

03

Provided new conditions for spectral theorems in operator classes

Abstract

The main objective of this work is to study generalized Browder's and Weyl's theorems for the multiplication operators $L_{A}$ and $R_{B}$ and for the elementary operator $τ_{A, B} = L_{A} R_{B}$ .

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Taxonomy

TopicsMatrix Theory and Algorithms · Holomorphic and Operator Theory · Algebraic and Geometric Analysis