Some results about EP modular operators

A bounded adjointable operator in Hilbert C*-modules is called EP if ranges of T and have the same closure. This definition is employed to achieve a new characterization of EP operators. We show that the anticommutator of EP operators is again an EP operator. It follows that the product of commuting...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 70; no. 18; pp. 3490 - 3496
Main Authors Mohammadzadeh Karizaki, M., Djordjević, D. S., Hosseini, A., Jalaeian, M.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 12.12.2022
Taylor & Francis Ltd
Subjects
EP modular operator
Hilbert
module
Operators
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Summary:A bounded adjointable operator in Hilbert C*-modules is called EP if ranges of T and have the same closure. This definition is employed to achieve a new characterization of EP operators. We show that the anticommutator of EP operators is again an EP operator. It follows that the product of commuting EP operators is an EP operator. Some other conditions implying the product of EP operators to be an EP operator are presented. Finally, we prove that for EP operators S, T equality holds.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2020.1844613