Weighted 1MP and MP1 inverses for operators-Reference-Cited by-同舟云学术

Weighted 1MP and MP1 inverses for operators

Published:2024-04-01 Issue:2 Volume:74 Page:437-450
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Mosić Dijana¹,Marovt Janko²³

Affiliation:

1. Faculty of Sciences and Mathematics University of Niš Box 224 Niš Serbia

2. University of Maribor Faculty of Economics and Business Razlagova 14 Maribor Slovenia

3. IMFM Jadranska 19 Ljubljana Slovenia

Abstract

Abstract The main aim of this paper is to extend the concepts of the 1MP and MP1 inverses defined for rectangular complex matrices. We present the weighted 1MP and MP1 inverses for a bounded linear operator between two Hilbert spaces as two new kinds of generalized inverses. The notions of the weighted 1MP and MP1 inverses are new in the context of rectangular complex matrices too. We establish a number of characterizations and some representations of the weighted 1MP and MP1 inverses. Several operator equations are solved applying the weighted 1MP and MP1 inverses. A special case of one of these equations is the normal equation which is related with the least-squares solution. As consequences of our results, we obtain new properties of the 1MP and MP1 inverses.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/ms-2024-0033/pdf

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