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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].

References [Enhancements On Off] (What's this?)

  • [1] E. Albrecht, Funktionalkalküle in mehreren veränderlichen, Ph.D. Dissertation, Mainz Univ., 1972.
  • [2] I. Colojoară and C. Foiaş, Theory of generalized spectral operators, Gordon and Breach, New York, 1968. MR 0394282 (52:15085)
  • [3] N. Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321-354. MR 0063563 (16:142d)
  • [4] Ş, Frunză, The Taylor spectrum and spectral decompositions, J. Functional Analysis 19 (1975), 390-421. MR 0394259 (52:15062)
  • [5] -, On Taylor functional calculus, Studia Math. 52 (1974), 239-242. MR 0361864 (50:14307)
  • [6] J. L. Taylor, A joint spectrum for several commuting operators, J. Functional Analysis 6 (1970), 172-191. MR 0268706 (42:3603)
  • [7] -, Analytic functional calculus for several commuting operators, Acta Math. 125 (1970), 1-38. MR 0271741 (42:6622)

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Keywords: Commuting system of operators, spectrum, local spectrum, differential form, cohomology, spectral hull, Stokes' theorem
Article copyright: © Copyright 1978 American Mathematical Society

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