Stability of the local spectrum

Bermúdez, Teresa; González, Manuel; Martinón, Antonio

doi:10.1090/S0002-9939-97-03477-1

Stability of the local spectrum
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by Teresa Bermúdez, Manuel González and Antonio Martinón PDF

Proc. Amer. Math. Soc. 125 (1997), 417-425 Request permission

Abstract:

We give some conditions implying the equality of local spectra \begin{equation*} \sigma (x, T)=\sigma (f[T]x, T), \end{equation*} where $T:X \to X$ 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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