Generalized weighted EP elements in Banach algebras
H. Chen, M. Sheibani
TL;DR
This paper introduces a new class of weighted generalized inverses in Banach *-algebras, extending EP and *-DMP elements, and explores their properties and characterizations.
Contribution
It defines weighted EP elements in Banach *-algebras and provides their characterizations and properties, including core-EP decomposition and polar-like properties.
Findings
Characterization of weighted EP elements
Core-EP decomposition for weighted EP elements
Properties of weighted *-DMP elements
Abstract
We propose a new class of generalized inverses with weights, which represent a natural extension of EP (Moore-Penrose) and *-DMP (Drazin-Moore-Penrose) elements in a Banach *-algebra. This paper presents various characteristics of weighted EP elements. Moreover, we characterize the weighted EP element through the core-EP decomposition and a polar-like property. Finally, we explore weighted *-DMP elements and uncover several new properties of *-DMP elements.
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Taxonomy
TopicsFormal Methods in Verification · Matrix Theory and Algorithms · Dynamics and Control of Mechanical Systems