On the Moore-Penrose inverse in C*-algebras.

Enrico Boasso

Extracta Mathematicae (2006)

  • Volume: 21, Issue: 2, page 93-106
  • ISSN: 0213-8743

Abstract

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In this article, two results regarding the Moore-Penrose inverse in the frame of C*-algebras are considered. In first place, a characterization of the so-called reverse order law is given, which provides a solution of a problem posed by M. Mbekhta. On the other hand, Moore-Penrose hermitian elements, that is C*-algebra elements which coincide with their Moore-Penrose inverse, are introduced and studied. In fact, these elements will be fully characterized both in the Hilbert space and in the C*-algebra setting. Furthermore, it will be proved that an element is normal and Moore-Penrose hermitian if and only if it is a hermitian partial isometry.

How to cite

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Boasso, Enrico. "On the Moore-Penrose inverse in C*-algebras.." Extracta Mathematicae 21.2 (2006): 93-106. <http://eudml.org/doc/41853>.

@article{Boasso2006,
abstract = {In this article, two results regarding the Moore-Penrose inverse in the frame of C*-algebras are considered. In first place, a characterization of the so-called reverse order law is given, which provides a solution of a problem posed by M. Mbekhta. On the other hand, Moore-Penrose hermitian elements, that is C*-algebra elements which coincide with their Moore-Penrose inverse, are introduced and studied. In fact, these elements will be fully characterized both in the Hilbert space and in the C*-algebra setting. Furthermore, it will be proved that an element is normal and Moore-Penrose hermitian if and only if it is a hermitian partial isometry.},
author = {Boasso, Enrico},
journal = {Extracta Mathematicae},
keywords = {Algebra de operadores; C*-álgebras; regular element; Moore-Penrose inverse; Moore-Penrose Hermitian element; -algebra; reverse order law},
language = {eng},
number = {2},
pages = {93-106},
title = {On the Moore-Penrose inverse in C*-algebras.},
url = {http://eudml.org/doc/41853},
volume = {21},
year = {2006},
}

TY - JOUR
AU - Boasso, Enrico
TI - On the Moore-Penrose inverse in C*-algebras.
JO - Extracta Mathematicae
PY - 2006
VL - 21
IS - 2
SP - 93
EP - 106
AB - In this article, two results regarding the Moore-Penrose inverse in the frame of C*-algebras are considered. In first place, a characterization of the so-called reverse order law is given, which provides a solution of a problem posed by M. Mbekhta. On the other hand, Moore-Penrose hermitian elements, that is C*-algebra elements which coincide with their Moore-Penrose inverse, are introduced and studied. In fact, these elements will be fully characterized both in the Hilbert space and in the C*-algebra setting. Furthermore, it will be proved that an element is normal and Moore-Penrose hermitian if and only if it is a hermitian partial isometry.
LA - eng
KW - Algebra de operadores; C*-álgebras; regular element; Moore-Penrose inverse; Moore-Penrose Hermitian element; -algebra; reverse order law
UR - http://eudml.org/doc/41853
ER -

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