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

On the localization of the spectrum for systems of operators


Author: Ştefan Frunză
Journal: Proc. Amer. Math. Soc. 69 (1978), 233-239
MSC: Primary 47A10; Secondary 47A60, 47B40
MathSciNet review: 0477810
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Abstract: Let $ a = ({a_1}, \ldots ,{a_n})$ be a commuting system of linear continuous operators on a complex Banach space X. We show that, for any $ x \in X$, the local analytic spectrum $ \sigma (a,x)$ [1] is contained in the spectral hull of the local spectrum $ {\text{sp}}(a,x)$ [4].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0477810-6
PII: S 0002-9939(1978)0477810-6
Keywords: Commuting system of operators, spectrum, local spectrum, differential form, cohomology, spectral hull, Stokes' theorem
Article copyright: © Copyright 1978 American Mathematical Society