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

Studia Mathematica (2000)

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

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topKoliha, 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

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- [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] S. L. Campbell and C. D. Meyer, Generalized Inverses of Linear Transformations, Pitman, London, 1979. Zbl0417.15002
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- [6] R. E. Harte and M. Mbekhta, Generalized inverses in C*-algebras II, ibid. 106 (1993), 129-138. Zbl0810.46063
- [7] R. Hartwig and I. J. Katz, On products of EP matrics, Linear Algebra Appl. 252 (1997), 339-345. Zbl0868.15015
- [8] I. J. Katz, Weigman type theorems for $E{P}_{r}$ matrices, Duke Math. J. 32 (1965), 423-428.
- [9] J. J. Koliha, A generalized Drazin inverse, Glasgow Math. J. 38 (1996), 367-381. Zbl0897.47002
- [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] J. J. Koliha, A simple proof of the product theorem for EP matrices, Linear Algebra Appl. 294 (1999), 213-215. Zbl0938.15017
- [12] I. Marek and K. Žitný, Matrix Analysis for Applied Sciences, Vol. 2, Teubner, Leipzig, 1986. Zbl0613.15002
- [13] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406-413. Zbl0065.24603
- [14] E. T. Wong, Does the generalized inverse of A commute with A?, Math. Mag. 59 (1986), 230-232. Zbl0611.15007
- [15] D. Djordjević, Products of EP operators on Hilbert spaces, Proc. Amer. Math. Soc., to appear.
- [16] G. Lešnjak, Semigroups of EP linear transformations, Linear Algebra Appl. 304 (2000), 109-118. Zbl0946.15009

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