Common operator properties

of the linear operators and

Author:
Bruce A. Barnes

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1055-1061

MSC (1991):
Primary 47A10, 47A60, 47B30

MathSciNet review:
1443814

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and be bounded linear operators defined on Banach spaces, , . When , then the operators and have many basic operator properties in common. This situation is studied in this paper.

**[B1]**Bruce A. Barnes,*The spectral and Fredholm theory of extensions of bounded linear operators*, Proc. Amer. Math. Soc.**105**(1989), no. 4, 941–949. MR**955454**, 10.1090/S0002-9939-1989-0955454-4**[B2]**Bruce A. Barnes,*Linear operators with a normal factorization through Hilbert space*, Acta Sci. Math. (Szeged)**56**(1992), no. 1-2, 125–146. MR**1204747****[BD]**Frank F. Bonsall and John Duncan,*Complete normed algebras*, Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80. MR**0423029****[CPY]**S. R. Caradus, W. E. Pfaffenberger, and Bertram Yood,*Calkin algebras and algebras of operators on Banach spaces*, Marcel Dekker, Inc., New York, 1974. Lecture Notes in Pure and Applied Mathematics, Vol. 9. MR**0415345****[J]**K. Jörgens,*Linear Integral Operators*, Pitman, Boston, 1982. MR83j:45001**[P]**Theodore W. Palmer,*Banach algebras and the general theory of *-algebras. Vol. I*, Encyclopedia of Mathematics and its Applications, vol. 49, Cambridge University Press, Cambridge, 1994. Algebras and Banach algebras. MR**1270014****[R]**Charles E. Rickart,*General theory of Banach algebras*, The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR**0115101****[Rg]**J. Ringrose,*Compact Non-Self-Adjoint Operators*, Van Nostrand Reinhold Math. Studies**35**, London, 1971.**[TL]**Angus Ellis Taylor and David C. Lay,*Introduction to functional analysis*, 2nd ed., John Wiley & Sons, New York-Chichester-Brisbane, 1980. MR**564653**

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Additional Information

**Bruce A. Barnes**

Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403

Email:
barnes@math.uoregon.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-98-04218-X

Keywords:
Spectrum,
closed range,
Fredholm operator,
poles of the resolvent

Received by editor(s):
February 22, 1996

Received by editor(s) in revised form:
September 23, 1996

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society