On generalized Weyl operators

Author:
Dragan S. Djordjevic

Journal:
Proc. Amer. Math. Soc. **130** (2002), 81-84

MSC (2000):
Primary 47A53, 47A55

DOI:
https://doi.org/10.1090/S0002-9939-01-06081-6

Published electronically:
April 26, 2001

MathSciNet review:
1855623

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Abstract | References | Similar Articles | Additional Information

The ``generalized Weyl'' operators between two Hilbert spaces are taken to be those with closed range for which the null space and that of the adjoint are of equal Hilbert space dimension. We show that products of two of these which happen to have closed range, and finite rank perturbation of these, are also generalized Weyl.

**[1]**R. H. Bouldin,*The product of operators with closed range*, Tôhoku Math. J.**25**(1973), 359-363. MR**48:4768****[2]**R. H. Bouldin,*Generalizations of semi-Fredholm operators*, Proc. Amer. Math. Soc.**123**(1995), 3757-3764. MR**96i:47020****[3]**L. Burlando,*Approximation by semi-Fredholm and semi-**-Fredholm operators in Hilbert spaces of arbitrary dimension*, Acta Sci. Math. (Szeged)**65**(1999), 217-275. MR**2000j:47020****[4]**L. Burlando,*On the weighted reduced minimum modulus*, Proceeding of the 17 Conference in Operator Theory (Timisoara, 1998) (2000), 47-66. CMP**2000:17****[5]**S. R. Caradus,*Generalized Inverses and Operator Theory*, Queen's paper in pure and applied mathematics, Queen's University, Kingston, Ontario, 1978.**[6]**S. R. Caradus, W. E. Pfaffenberger and B. Yood,*Calkin Algebras and Algebras of Operators on Banach Spaces*, Marcel Dekker, New York, 1974.**[7]**R. E. Harte,*Regular boundary elements*, Proc. Amer. Math. Soc.**99**(1987), 328-330. MR**88d:46088****[8]**R. E. Harte,*Invertibility and Singularity for Bounded Linear Operators*, New York, Marcel Dekker, 1988. MR**89d:47001****[9]**R. E. Harte,*The ghost of an index theorem*, Proc. Amer. Math. Soc.**106**(1989), 1031-1033. MR**92j:47029****[10]**R. E. Harte and H. Raubenheimer,*Fredholm, Weyl and Browder theory III*, Proc. R. Ir. Acad.**95A**(1995), 11-16. MR**96i:47002****[11]**T. Kato,*Perturbation Theory for Linear Operators*, Springer-Verlag, Berlin-Heidelberg-New York, 1976. MR**53:11389****[12]**J. J. Koliha,*The product of relatively regular operators*, Comm. Math. Univ. Carolinae**16, 3**(1975), 531-539. MR**52:1373**

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Additional Information

**Dragan S. Djordjevic**

Affiliation:
Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, Ćirila i Metodija 2 18000 Niš, Yugoslavia

Email:
dragan@pmf.pmf.ni.ac.yu, ganedj@eunet.yu

DOI:
https://doi.org/10.1090/S0002-9939-01-06081-6

Keywords:
Generalized Weyl operators,
products of generalized Weyl operators,
perturbations

Received by editor(s):
May 17, 2000

Published electronically:
April 26, 2001

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2001
American Mathematical Society