Riesz points of upper triangular operator matrices
Author:
Bruce A. Barnes
Journal:
Proc. Amer. Math. Soc. 133 (2005), 13431347
MSC (2000):
Primary 47A10
Published electronically:
December 15, 2004
MathSciNet review:
2111940
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Abstract 
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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.
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Bruce
A. Barnes, Riesz points and Weyl’s theorem, Integral
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A. Barnes, G.
J. Murphy, M.
R. F. Smyth, and T.
T. West, Riesz and Fredholm theory in Banach algebras,
Research Notes in Mathematics, vol. 67, Pitman (Advanced Publishing
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Mohamed
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(2004d:47009), http://dx.doi.org/10.1090/S000299390306862X
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Min Han, A note on Weyl’s theorem for
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2543–2547. MR 1974653
(2004a:47002), http://dx.doi.org/10.1090/S0002993902068089
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 [B1]
 B. Barnes, Riesz points and Weyl's Theorem, Integral Equ. and Operator Theory 34 (1999), 187196. MR 1694707 (2000d:47006)
 [B2]
 B. Barnes, The spectral theory of upper triangular matrices with entries in a Banach algebra, Math. Nachr. 241 (2002), 520. MR 1912373 (2003e:47004)
 [BMSW]
 B. Barnes, G. Murphy, R. Smyth, and T.T. West, Riesz and Fredholm Theory in Banach Algebras, Pitman, BostonLondonMelbourne, 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), 30833088. 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), 25432547. MR 1974653 (2004a:47002)
 [HL]
 R. Harte and W. Lee, Another note on Weyl's Theorem, Trans. Amer. Math. Soc. 349 (1997), 21152124. MR 1407492 (98j:47024)
 [L]
 W. Lee, Weyl's spectra of operator matrices, Proc. Amer. Math. Soc. 129 (2000), 131138.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:
http://dx.doi.org/10.1090/S0002993904078116
PII:
S 00029939(04)078116
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.
