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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stability of the local spectrum


Authors: Teresa Bermúdez, Manuel González and Antonio Martinón
Journal: Proc. Amer. Math. Soc. 125 (1997), 417-425
MSC (1991): Primary 47A11, 47A60
MathSciNet review: 1343681
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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: http://dx.doi.org/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
Article copyright: © Copyright 1997 American Mathematical Society