H. Elbjaoui, E. H. Zerouali, "Local spectral theory for 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 operator matrices
We discuss the spectral properties of the operator defined by , where , , , and , are complex Banach spaces. We prove that for all . 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.