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Stability of the local spectrum |
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| Authors: | Teresa Bermú dez Manuel Gonzá lez Antonio Martinó n |
| Affiliation: | Departamento de Análisis Matemático, Universidad de La Laguna, La Laguna, Spain ; Departamento de Matemáticas, Universidad de Cantabria, Santander, Spain Antonio Martinón ; Departamento de Análisis Matemático, Universidad de La Laguna, La Laguna, Spain |
| Abstract: | We give some conditions implying the equality of local spectra
where |
| Keywords: | Local spectrum holomorphic functional calculus meromorphic functional calculus |
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![begin{equation*}sigma (x, T)=sigma (f[T]x, T), end{equation*}](http://www.ams.org/proc/1997-125-02/S0002-9939-97-03477-1/gif-abstract/img1.gif)
is a (bounded linear) operator on a complex Banach space 
and ![$f[T]x$](http://www.ams.org/proc/1997-125-02/S0002-9939-97-03477-1/gif-abstract/img4.gif)
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.