Products of EP operators on Hilbert spaces

Author:
Dragan S. Djordjevic

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1727-1731

MSC (2000):
Primary 47A05, 15A09

DOI:
https://doi.org/10.1090/S0002-9939-00-05701-4

Published electronically:
October 31, 2000

MathSciNet review:
1814103

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Abstract | References | Similar Articles | Additional Information

Abstract: A Hilbert space operator is called the EP operator if the range of is equal to the range of its adjoint . 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.

**[1]**T. S. Baskett and I. J. Katz,*Theorems on products of**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**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 Niš, Ćirila i Metodija 2, 18000 Niš, Yugoslavia

Email:
dragan@archimed.filfak.ni.ac.yu, dragan@filfak.filfak.ni.ac.yu

DOI:
https://doi.org/10.1090/S0002-9939-00-05701-4

Keywords:
EP operators,
generalized inverses

Received by editor(s):
May 4, 1999

Received by editor(s) in revised form:
September 17, 1999

Published electronically:
October 31, 2000

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2000
American Mathematical Society