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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: October 31, 2000
MathSciNet review: 1814103
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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.


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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: http://dx.doi.org/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
Published electronically: October 31, 2000
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2000 American Mathematical Society