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Finite Rank Operators and Functional Calculus on Hilbert Modules over Abelian C*-Algebras
Published online by Cambridge University Press: 20 November 2018
Abstract
We consider the problem: If K is a compact normal operator on a Hilbert module E, and f ∈ C0(SpK) is a function which is zero in a neighbourhood of the origin, is f(K) of finite rank? We show that this is the case if the underlying C*-algebra is abelian, and that the range of f(K) is contained in a finitely generated projective submodule of E.
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- Copyright © Canadian Mathematical Society 1997
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