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Search: MSC category 55R50 ( Stable classes of vector space bundles, $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX} )

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1. CMB 1997 (vol 40 pp. 193)

Kucerovsky, Dan
Finite rank operators and functional calculus on Hilbert modules over abelian $C^{\ast}$-algebras
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 $E$.

Categories:55R50, 47A60, 47B38

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