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One-sided generalized Drazin-Riesz and one-sided generalized Drazin-meromorphic invertible operators

Snežana Č. Živković-Zlatanović

Abstract

The aim of this paper is to introduce and study left and right versions of the class of generalized Drazin-Riesz invertible operators, as well as left and right versions of the class of generalized Drazin-meromorphic invertible operators.

One-sided generalized Drazin-Riesz and one-sided generalized Drazin-meromorphic invertible operators

Abstract

The aim of this paper is to introduce and study left and right versions of the class of generalized Drazin-Riesz invertible operators, as well as left and right versions of the class of generalized Drazin-meromorphic invertible operators.
Paper Structure (6 sections, 39 theorems, 55 equations)

This paper contains 6 sections, 39 theorems, 55 equations.

Table of Contents

  1. Introduction and background
  2. Definitions
  3. Preiliminary results
  4. Left and right generalized Drazin-Riesz invertible operators
  5. Left and right generalized Drazin-meromorphic invertible operators
  6. Spectra

Key Result

Lemma 3.1

ZS Let $X=X_1\oplus X_2\oplus\dots\oplus X_n$ where $X_1,\ X_2,\dots ,X_n$ are closed subspaces of $X$ and let $M_i$ be a subset of $X_i$, $i=1,\dots,n$. Then the set $M_1+ M_2+\dots+ M_n$ is closed if and only if $M_i$ is closed for each $i\in\{1,\dots,n\}$.

Theorems & Definitions (77)

  • Lemma 3.1
  • Lemma 3.2
  • Lemma 3.3
  • Lemma 3.4
  • Lemma 3.5
  • proof
  • Lemma 3.6
  • Lemma 3.7
  • proof
  • Lemma 3.8
  • ...and 67 more