Riesz points of upper triangular operator matrices

Author:
Bruce A. Barnes

Journal:
Proc. Amer. Math. Soc. **133** (2005), 1343-1347

MSC (2000):
Primary 47A10

DOI:
https://doi.org/10.1090/S0002-9939-04-07811-6

Published electronically:
December 15, 2004

MathSciNet review:
2111940

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Abstract | References | Similar Articles | Additional Information

Abstract: Two results are proved which concern Riesz points of upper triangular operator matrices. Applications are made to questions involving when Weyl's Theorem holds for an upper triangular operator matrix.

**[B1]**B. Barnes, Riesz points and Weyl's Theorem, Integral Equ. and Operator Theory 34 (1999), 187-196. MR**1694707 (2000d:47006)****[B2]**B. Barnes, The spectral theory of upper triangular matrices with entries in a Banach algebra, Math. Nachr. 241 (2002), 5-20. MR**1912373 (2003e:47004)****[BMSW]**B. Barnes, G. Murphy, R. Smyth, and T.T. West, Riesz and Fredholm Theory in Banach Algebras, Pitman, Boston-London-Melbourne, 1982. MR**0668516 (84a:46108)****[BB]**M. Barraa and M. Boumazgour, A note on the spectrum of an upper triangular operator matrix, Proc. Amer. Math. Soc. 131 (2003), 3083-3088. MR**1993217 (2004d:47009)****[DH]**S. Djordjevic and Y. Han, A note on Weyl's Theorem for operator matrices, Proc. Amer. Math. Soc. 131 (2002), 2543-2547. MR**1974653 (2004a:47002)****[HL]**R. Harte and W. Lee, Another note on Weyl's Theorem, Trans. Amer. Math. Soc. 349 (1997), 2115-2124. MR**1407492 (98j:47024)****[L]**W. Lee, Weyl's spectra of operator matrices, Proc. Amer. Math. Soc. 129 (2000), 131-138.MR**1784020 (2001f:47003)**

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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:
https://doi.org/10.1090/S0002-9939-04-07811-6

Keywords:
Riesz point,
upper triangular operator matrix,
Weyl's Theorem

Received by editor(s):
November 4, 2003

Published electronically:
December 15, 2004

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.