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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

Dan Kucerovsky
Dan Kucerovsky*
Affiliation:
Université Paris 6 Laboratoire de Mathematiques Fondamentales aile 46–00, (URA 747) 4, pl. Jussieu F7525 Paris Cedex 5 France, e-mail: kucerov@mathp6.jussieu.fr
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Abstract

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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.

Keywords

Primary: 55R5047A6047B38
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 2 , 01 June 1997 , pp. 193 - 197
Copyright
Copyright © Canadian Mathematical Society 1997

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