Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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
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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