Elements of C*-algebras commuting with their Moore-Penrose inverse

J. Koliha

Studia Mathematica (2000)

  • Volume: 139, Issue: 1, page 81-90
  • ISSN: 0039-3223

Abstract

top
We give new necessary and sufficient conditions for an element of a C*-algebra to commute with its Moore-Penrose inverse. We then study conditions which ensure that this property is preserved under multiplication. As a special case of our results we recover a recent theorem of Hartwig and Katz on EP matrices.

How to cite

top

Koliha, J.. "Elements of C*-algebras commuting with their Moore-Penrose inverse." Studia Mathematica 139.1 (2000): 81-90. <http://eudml.org/doc/216712>.

@article{Koliha2000,
abstract = {We give new necessary and sufficient conditions for an element of a C*-algebra to commute with its Moore-Penrose inverse. We then study conditions which ensure that this property is preserved under multiplication. As a special case of our results we recover a recent theorem of Hartwig and Katz on EP matrices.},
author = {Koliha, J.},
journal = {Studia Mathematica},
keywords = {C*-algebra; Moore-Penrose inverse; Drazin inverse; -algebra; regular elements; EP matrices},
language = {eng},
number = {1},
pages = {81-90},
title = {Elements of C*-algebras commuting with their Moore-Penrose inverse},
url = {http://eudml.org/doc/216712},
volume = {139},
year = {2000},
}

TY - JOUR
AU - Koliha, J.
TI - Elements of C*-algebras commuting with their Moore-Penrose inverse
JO - Studia Mathematica
PY - 2000
VL - 139
IS - 1
SP - 81
EP - 90
AB - We give new necessary and sufficient conditions for an element of a C*-algebra to commute with its Moore-Penrose inverse. We then study conditions which ensure that this property is preserved under multiplication. As a special case of our results we recover a recent theorem of Hartwig and Katz on EP matrices.
LA - eng
KW - C*-algebra; Moore-Penrose inverse; Drazin inverse; -algebra; regular elements; EP matrices
UR - http://eudml.org/doc/216712
ER -

References

top
  1. [1] T. S. Baskett and I. J. Katz, Theorems on products of E P r matrices, Linear Algebra Appl. 2 (1969), 87-103. Zbl0179.05104
  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. L. Campbell and C. D. Meyer, Generalized Inverses of Linear Transformations, Pitman, London, 1979. Zbl0417.15002
  4. [4] M. P. Drazin, Pseudo-inverse in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506-514. Zbl0083.02901
  5. [5] R. E. Harte and M. Mbekhta, On generalized inverses in C*-algebras, Studia Math. 103 (1992), 71-77. Zbl0810.46062
  6. [6] R. E. Harte and M. Mbekhta, Generalized inverses in C*-algebras II, ibid. 106 (1993), 129-138. Zbl0810.46063
  7. [7] R. Hartwig and I. J. Katz, On products of EP matrics, Linear Algebra Appl. 252 (1997), 339-345. Zbl0868.15015
  8. [8] I. J. Katz, Weigman type theorems for E P r matrices, Duke Math. J. 32 (1965), 423-428. 
  9. [9] J. J. Koliha, A generalized Drazin inverse, Glasgow Math. J. 38 (1996), 367-381. Zbl0897.47002
  10. [10] J. J. Koliha, The Drazin and Moore-Penrose inverse in C*-algebras, Proc. Roy. Irish Acad. Sect. A 99 (1999), 17-27. Zbl0943.46031
  11. [11] J. J. Koliha, A simple proof of the product theorem for EP matrices, Linear Algebra Appl. 294 (1999), 213-215. Zbl0938.15017
  12. [12] I. Marek and K. Žitný, Matrix Analysis for Applied Sciences, Vol. 2, Teubner, Leipzig, 1986. Zbl0613.15002
  13. [13] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406-413. Zbl0065.24603
  14. [14] E. T. Wong, Does the generalized inverse of A commute with A?, Math. Mag. 59 (1986), 230-232. Zbl0611.15007
  15. [15] D. Djordjević, Products of EP operators on Hilbert spaces, Proc. Amer. Math. Soc., to appear. 
  16. [16] G. Lešnjak, Semigroups of EP linear transformations, Linear Algebra Appl. 304 (2000), 109-118. Zbl0946.15009

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.