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Additive results of group inverses in Banach algebras

Dayong Liu, Huanyin Chen

Abstract

In this paper, we present new presentations of group inverse for the sum of two group invertible elements in a Banach algebra. We then apply these results to block complex matrices. The group invertibility of certain block complex matrices is thereby obtained.

Additive results of group inverses in Banach algebras

Abstract

In this paper, we present new presentations of group inverse for the sum of two group invertible elements in a Banach algebra. We then apply these results to block complex matrices. The group invertibility of certain block complex matrices is thereby obtained.
Paper Structure (4 sections, 11 theorems, 54 equations)

This paper contains 4 sections, 11 theorems, 54 equations.

Table of Contents

  1. Introduction
  2. main results
  3. applications
  4. Disclosure statement

Key Result

Theorem 2.1

Let $a,b\in \mathcal{A}^{\#}, \lambda\in {\Bbb C}.$ If $abb^{\#}=\lambda baa^{\#}$, then $a+b\in \mathcal{A}^{\#}$. In this case,

Theorems & Definitions (23)

  • Theorem 2.1
  • proof
  • Corollary 2.2
  • proof
  • Corollary 2.3
  • proof
  • Theorem 2.4
  • proof
  • Corollary 2.5
  • proof
  • ...and 13 more