Generalized inverses in C*-algebras II

Robin Harte; Mostafa Mbekhta

Studia Mathematica (1993)

  • Volume: 106, Issue: 2, page 129-138
  • ISSN: 0039-3223

Abstract

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Commutativity and continuity conditions for the Moore-Penrose inverse and the "conorm" are established in a C*-algebra; moreover, spectral permanence and B*-properties for the conorm are proved.

How to cite

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Harte, Robin, and Mbekhta, Mostafa. "Generalized inverses in C*-algebras II." Studia Mathematica 106.2 (1993): 129-138. <http://eudml.org/doc/216008>.

@article{Harte1993,
abstract = {Commutativity and continuity conditions for the Moore-Penrose inverse and the "conorm" are established in a C*-algebra; moreover, spectral permanence and B*-properties for the conorm are proved.},
author = {Harte, Robin, Mbekhta, Mostafa},
journal = {Studia Mathematica},
keywords = {commutativity; conorm; continuity; Moore-Penrose inverse; - algebra; spectral permanence},
language = {eng},
number = {2},
pages = {129-138},
title = {Generalized inverses in C*-algebras II},
url = {http://eudml.org/doc/216008},
volume = {106},
year = {1993},
}

TY - JOUR
AU - Harte, Robin
AU - Mbekhta, Mostafa
TI - Generalized inverses in C*-algebras II
JO - Studia Mathematica
PY - 1993
VL - 106
IS - 2
SP - 129
EP - 138
AB - Commutativity and continuity conditions for the Moore-Penrose inverse and the "conorm" are established in a C*-algebra; moreover, spectral permanence and B*-properties for the conorm are proved.
LA - eng
KW - commutativity; conorm; continuity; Moore-Penrose inverse; - algebra; spectral permanence
UR - http://eudml.org/doc/216008
ER -

References

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  1. [1] C. Apostol, The reduced minimum modulus, Michigan Math. J. 32 (1985), 279-294. 
  2. [2] K. G. Brock, A note on commutativity of a linear operator and its Moore-Penrose inverse, Numer. Funct. Anal. Optim. 11 (1990), 673-678. Zbl0729.47001
  3. [3] S. R. Caradus, Generalized Inverses and Operator Theory, Queen's Papers in Pure and Appl. Math. 50, Queen's Univ., Kingston, Ont., 1978. 
  4. [4] C. W. Groetsch, Representations of the generalized inverse, J. Math. Anal. Appl. 49 (1975), 154-157. 
  5. [5] P. R. Halmos, A Hilbert Space Problem Book, Van Nostrand, New York 1967. 
  6. [6] R. E. Harte, Invertibility and Singularity, Dekker, New York 1988. 
  7. [7] R. E. Harte and M. Mbekhta, On generalized inverses in C*-algebras, Studia Math. 103 (1992), 71-77. Zbl0810.46062
  8. [8] R. E. Harte and M. Ó Searcóid, Positive elements and the B* condition, Math. Z. 193 (1986), 1-9. Zbl0611.46061
  9. [9] T. Kato, Perturbation Theory for Linear Operators, Springer, New York 1966. 
  10. [10] M. Mbekhta, Conorme et inverse généralisé dans les C*-algèbres, Canad. Math. Bull. 35 (1992), 515-522. 
  11. [11] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406-413. Zbl0065.24603
  12. [12] A. Pietsch, Operator Ideals, North-Holland, 1980. 

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