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Finite rank operators and functional calculus on Hilbert modules over abelian $C^{\ast}$-algebras |
Canad. Math. Bull. 40(1997), 193-197
Published:1997-06-01
Printed: Jun 1997
Printed: Jun 1997
- Dan Kucerovsky
Abstract
We consider the problem: If $K$ is a compact normal operator on a Hilbert
module $E$, and $f\in C_0(\Sp K)$ 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 $C^{\ast}$-algebra is abelian, and that
the range of $f(K)$ is contained in a finitely generated projective
submodule of $E$.
| MSC Classifications: |
55R50 - Stable classes of vector space bundles, $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX} 47A60 - Functional calculus 47B38 - Operators on function spaces (general) |