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1 results

  • Finite Rank Operators and Functional Calculus on Hilbert Modules over Abelian C*-Algebras

  • Dan Kucerovsky
  • Journal:
    Canadian Mathematical Bulletin / Volume 40 / Issue 2 / 01 June 1997
    Published online by Cambridge University Press:
    20 November 2018, pp. 193-197
    Print publication:
    01 June 1997
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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.