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Joint spectra of operators on Banach space

Published online by Cambridge University Press:  18 May 2009

Muneo Chō
Muneo Chō
Affiliation:
Department of Mathematics, Joetsu University of Education, Joetsu 943, Japan
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Let X be a complex Banach space. We denote by B(X) the algebra of all bounded linear operators on X. Let = (T1, …, Tn) be a commuting n-tuple of operators on X. And let στ() and σ″() by Taylor's joint spectrum and the doubly commutant spectrum of , respectively. We refer the reader to Taylor [8] for the definition of στ() and σ″(), A point z = (z1,…, zn) of ℂn is in the joint approximate point spectrum σπ() of if there exists a sequence {xk} of unit vectors in X such that

∥(Ti – zi)xk∥→0 as k → ∞ for i = 1, 2,…, n.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 28 , Issue 1 , January 1986 , pp. 69 - 72
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

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