International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 893151 | https://doi.org/10.1155/S0161171203012043

H. Elbjaoui, E. H. Zerouali, "Local spectral theory for 2×2 operator matrices", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 893151, 6 pages, 2003. https://doi.org/10.1155/S0161171203012043

Local spectral theory for 2×2 operator matrices

Received13 Feb 2001
Revised11 Jul 2001

Abstract

We discuss the spectral properties of the operator MC(XY) defined by MC:=(AC0B), where A(X), B(Y), C(Y,X), and X, Y are complex Banach spaces. We prove that (SASB)σ(MC)=σ(A)σ(B) for all C(Y,X). This allows us to give a partial positive answer to Question 3 of Du and Jin (1994) and generalizations of some results of Houimdi and Zguitti (2000). Some applications to the similarity problem are also given.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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