Preprint Article Version 1 This version is not peer-reviewed

Generalized core-EP inverse for triangular operator matrices

Version 1 : Received: 1 August 2024 / Approved: 2 August 2024 / Online: 4 August 2024 (23:35:06 CEST)

How to cite: Chen, H. Generalized core-EP inverse for triangular operator matrices. Preprints 2024, 2024080216. https://doi.org/10.20944/preprints202408.0216.v1 Chen, H. Generalized core-EP inverse for triangular operator matrices. Preprints 2024, 2024080216. https://doi.org/10.20944/preprints202408.0216.v1

Abstract

We investigate the existence and representation of the generalized core-EP inverse of some triangular matrices over a Banach algebra. Further, the general representations of the generalized core-EP inverse of a triangular matrix over a $C^*$-algebra are presented. As applications, the generalized core-EP inverses of some block operator matrices over Hilbert spaces are given.

Keywords

core inverse; core-EP inverse; generalized core-EP inverse; triangular matrix; Block operator matrix; Banach algebra.

Subject

Computer Science and Mathematics, Algebra and Number Theory

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