The Moore–Penrose Inverse and Product Decomposition of Idempotent Operators on Hilbert C*-Modules

Axioms 2026 Open access

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Authors: Wei Luo
DOI: 10.3390/axioms15020141
Cited by: 0

Abstract

We study the Moore–Penrose inverse of idempotent operators on Hilbert C*-modules. First, we extend the computation of the Moore–Penrose inverse of an idempotent operator and its difference from the range projection to this setting. This leads to an explicit formula for the Moore–Penrose inverse of the sum of an idempotent and its adjoint. Furthermore, we establish a decomposition of an idempotent operator into a product of two commuting idempotents and clarify the relationship between their Moore–Penrose inverses and that of the original operator. We also analyze spectral properties and operator norms, obtaining sharp norm bounds.

Fields of Study & Subjects

Advanced Operator Algebra Research Advanced Banach Space Theory Matrix Theory and Algorithms

Publication details

Journal / source
Axioms
Volume
15
Issue
2
Pages
141–141
Publication date
14 February 2026
Language
EN