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Local spectral theory and spectral inclusions

Published online by Cambridge University Press:  18 May 2009

Kjeld B. Laursen  and
Michael M. Neumann
Kjeld B. Laursen
Affiliation:
Mathematics Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark
Michael M. Neumann
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, P.O. Drawer Ma, Mississippi State, MS 39762, U.S.A.
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Suppose that T and S are continuous linear operators on complex Banach spaces X and Y, respectively, and that A is a non-zero continuous linear mapping from X to Y. If A intertwines T and S in the sense that SA = AT, then a classical result due to Rosenblum implies that the spectra σ(T) and σ(S) must overlap, see [12]. Actually, Davis and Rosenthal [5]have shown that the surjectivity spectrum σsu(T) will meet the approximate point spectrum σap(S) in this case (terms to be denned below). Further information about the relations between the two spectra and their finer structure becomes available when the intertwiner A is injective or has dense range, see [9], [12], [13].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 3 , September 1994 , pp. 331 - 343
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

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