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Stability of the local spectrum

Author(s): Teresa Bermúdez; Manuel González; Antonio Martinón
Journal: Proc. Amer. Math. Soc. 125 (1997), 417-425.
MSC (1991): Primary 47A11, 47A60
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Abstract: We give some conditions implying the equality of local spectra

\begin{equation*}\sigma (x, T)=\sigma (f[T]x, T), \end{equation*}

where $T:X \longrightarrow X$ is a (bounded linear) operator on a complex Banach space $X,$ and $f[T]x$ is defined by means of a local functional calculus. Moreover, we give conditions implying the stability of the local spectrum for the holomorphic and the meromorphic functional calculi.

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Additional Information:

Teresa Bermúdez
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, La Laguna, Spain
Email: tbermudez@ull.es

Manuel González
Affiliation: Departamento de Matemáticas, Universidad de Cantabria, Santander, Spain

Antonio Martinón
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, La Laguna, Spain

DOI: 10.1090/S0002-9939-97-03477-1
PII: S 0002-9939(97)03477-1
Keywords: Local spectrum, holomorphic functional calculus, meromorphic functional calculus
Received by editor(s): May 18, 1995
Additional Notes: Supported in part by DGICYT Grant PB 91-0307 (Spain)
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1997, American Mathematical Society

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The following works have cited this article

T. Bermúdez, M. González and A. Martinón, On the poles of the local resolvent , Math. Nachr. 193 (1998), 19-26. MR 99f:47006

T. Bermúdez, Meromorphic functional calculus and local spectral theory, Rocky Mountain Journal of Mathematics (2) 29 (1999), 437-447. MR 2000e:47029

R. Cross, Multivalued linear operators , Monographs and texbooks in pure and applied mathematics, vol. 213, Marcel Dekker , New York, 1998. MR 99j:47003

K. Laursen and M. Neumann, Introduction to local spectral theory, London Mathematical Society Monographs, Oxford University Press, 2000.

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