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A note on Weyl's theorem for operator matrices

Author(s): Slavisa V. Djordjevic; Young Min Han
Journal: Proc. Amer. Math. Soc. 131 (2003), 2543-2547.
MSC (2000): Primary 47A10, 47A55
Posted: November 27, 2002
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Abstract: When $A\in\mathcal B(X)$ and $B\in\mathcal B(Y)$ are given we denote by $M_C$ an operator acting on the Banach space $X\oplus Y$of the form

\begin{displaymath}M_{C}=\left (\begin{matrix}A&C 0&B\end{matrix}\right), \text{where} C\in \mathcal B(Y,X). \end{displaymath}

In this note we examine the relation of Weyl's theorem for $A\oplus B$ and $M_C$ through local spectral theory.

References:

1.
P. Aiena and O. Monsalve, Operators which do not have the single valued extension property, J. Math. Anal. Appl. 250 (2000), 435-448. MR 2001g:47005

2.
S.V. Djordjevic, B.P. Duggal and Y.M. Han, The single valued extension property and Weyl's theorem (preprint).

3.
H.K. Du and J. Pan, Perturbation of spectrums of $2\times2$ operator matrices, Proc. Amer. Math. Soc. 121 (1994), 761-766. MR 94i:47004

4.
J.K. Finch, The single valued extension property on a Banach space, Pacific J. Math. 58 (1975), 61-69. MR 51:11181

5.
J.K. Han, H.Y. Lee and W.Y. Lee, Invertible completions of $2\times 2$ upper triangular operator matrices, Proc. Amer. Math. Soc. 128 (2000), 119-123. MR 2000c:47003

6.
R.E. Harte, Invertibility and Singularity for Bounded Linear Operators, Dekker, New York, 1988. MR 89d:47001

7.
R.E. Harte and W.Y. Lee, Another note on Weyl's theorem, Trans. Amer. Math. Soc. 349 (1997), 2115-2124. MR 98j:47024

8.
M. Houimdi and H. Zguitti, Propriétés spectrales locales d'une matrice carree des operateurs, Acta Math. Vietnamica 25 (2000), 137-144. MR 2001d:47011

9.
J.J. Koliha, Isolated spectral points, Proc. Amer. Math. Soc. 124 (1996), 3417-3424. MR 97a:46057

10.
K.B. Laursen and M.M. Neumann, An Intruduction to Local Spectra Theory, London Mathematical Society Monographs, New Series 20, Clarendon Press, Oxford 2000. MR 2001k:47002

11.
W.Y. Lee, Weyl's theorem for operator matrices, Integral Equations and Operator Theory 32 (1998), 319-331. MR 99g:47023

12.
W.Y. Lee, Weyl's spectra of operator matrices, Proc. Amer. Math. Soc. 129 (2001), 131-138. MR 2001f:47003

13.
K.K. Oberai, Spectral mapping theorem for essential spectra, Rev. Roumaine Math. Pures Appl. 25 (1980), 365-373. MR 81j:47007

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Additional Information:

Slavisa V. Djordjevic
Affiliation: University of Nis, Faculty of Science, P.O. Box 91, 18000 Nis, Yugoslavia
Email: slavdj@pmf.pmf.ni.ac.yu

Young Min Han
Affiliation: Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242-1419
Email: yhan@math.uiowa.edu

DOI: 10.1090/S0002-9939-02-06808-9
PII: S 0002-9939(02)06808-9
Keywords: Upper triangular operator matrix, Weyl's theorem, single valued extension property
Received by editor(s): January 21, 2002
Received by editor(s) in revised form: March 27, 2002
Posted: November 27, 2002
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2002, American Mathematical Society

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