Annals of Functional Analysis

On m-generalized invertible operators on Banach spaces

Hamid Ezzahraoui

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Abstract

A bounded linear operator S on a Banach space X is called an m-left generalized inverse of an operator T for a positive integer m if

Tj=0m(1)j(mj)SmjTmj=0, and it is called an m-right generalized inverse of T if

Sj=0m(1)j(mj)TmjSmj=0. If T is both an m-left and an m-right generalized inverse of T, then it is said to be an m-generalized inverse of T.

This paper has two purposes. The first is to extend the notion of generalized inverse to m-generalized inverse of an operator on Banach spaces and to give some structure results. The second is to generalize some properties of m-partial isometries on Hilbert spaces to the class of m-left generalized invertible operators on Banach spaces. In particular, we study some cases in which a power of an m-left generalized invertible operator is again m-left generalized invertible.

Article information

Source
Ann. Funct. Anal., Volume 7, Number 4 (2016), 609-621.

Dates
Received: 13 March 2016
Accepted: 3 May 2016
First available in Project Euclid: 23 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.afa/1474652185

Digital Object Identifier
doi:10.1215/20088752-3660801

Mathematical Reviews number (MathSciNet)
MR3550939

Zentralblatt MATH identifier
06667757

Subjects
Primary: 47B48: Operators on Banach algebras
Secondary: 47B99: None of the above, but in this section

Keywords
$m$-isometry $m$-partial-isometry $m$-left inverse $m$-right inverse $m$-left generalized inverse $m$-right generalized inverse

Citation

Ezzahraoui, Hamid. On $m$ -generalized invertible operators on Banach spaces. Ann. Funct. Anal. 7 (2016), no. 4, 609--621. doi:10.1215/20088752-3660801. https://projecteuclid.org/euclid.afa/1474652185


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