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Products of EP operators on Hilbert spaces

Author(s): Dragan S. Djordjevic
Journal: Proc. Amer. Math. Soc. 129 (2001), 1727-1731.
MSC (2000): Primary 47A05, 15A09
Posted: October 31, 2000
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Abstract: A Hilbert space operator $A$ is called the EP operator if the range of $A$ is equal to the range of its adjoint $A^{*}$. In this article necessary and sufficient conditions are given for a product of two EP operators with closed ranges to be an EP operator with a closed range. Thus, a generalization of the well-known result of Hartwig and Katz (Linear Algebra Appl. 252 (1997), 339-345) is given.

References:

[1]
T. S. Baskett and I. J. Katz, Theorems on products of $EP_{r}$ matrices, Linear Algebra Appl. 2 (1969), 87-103. MR 40:4280

[2]
A. Ben-Israel and T. N. E. Greville, Generalized inverses: theory and applications, Wiley-Interscience, New York, 1974. MR 53:469

[3]
R. H. Bouldin, Generalized inverses and factorizations, Recent applications of generalized inverses, Pitman Ser. Res. Notes in Math., vol. 66, 1982, pp. 233-249. MR 83j:47001

[4]
S. R. Caradus, Generalized inverses and operator theory, Queen's paper in pure and applied mathematics, Queen's University, Kingston, Ontario, 1978. MR 81m:47003

[5]
R. E. Hartwig and I. J. Katz, On products of EP matrices, Linear Algebra Appl. 252 (1997), 339-345. MR 98a:15050

[6]
I. J. Katz, Weigmann type theorems for $EP_{r}$ matrices, Duke Math. J. 32 (1965), 423-427. MR 31:4804

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Additional Information:

Dragan S. Djordjevic
Affiliation: Department of Mathematics, Faculty of Philosophy, University of Nis, Cirila i Metodija 2, 18000 Nis, Yugoslavia
Email: dragan@archimed.filfak.ni.ac.yu, dragan@filfak.filfak.ni.ac.yu

DOI: 10.1090/S0002-9939-00-05701-4
PII: S 0002-9939(00)05701-4
Keywords: EP operators, generalized inverses
Received by editor(s): May 4, 1999
Received by editor(s) in revised form: September 17, 1999
Posted: October 31, 2000
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2000, American Mathematical Society

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