Geodesic
Finite Rank Operators and Functional Calculus on Hilbert Modules over Abelian C *-Algebras
Canadian mathematical bulletin, Tome 40 (1997) no. 2, pp. 193-197

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DOI

We consider the problem: If K is a compact normal operator on a Hilbert module E, and f ∈ C0 (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 *-algebra is abelian, and that the range of f(K) is contained in a finitely generated projective submodule of E.
DOI : 10.4153/CMB-1997-023-3
Mots-clés : Primary: 55R50, 47A60, 47B38 
Kucerovsky, Dan. Finite Rank Operators and Functional Calculus on Hilbert Modules over Abelian C *-Algebras. Canadian mathematical bulletin, Tome 40 (1997) no. 2, pp. 193-197. doi: 10.4153/CMB-1997-023-3
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     author = {Kucerovsky, Dan},
     title = {Finite {Rank} {Operators} and {Functional} {Calculus} on {Hilbert} {Modules} over {Abelian} {C} {*-Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {193--197},
     year = {1997},
     volume = {40},
     number = {2},
     doi = {10.4153/CMB-1997-023-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-023-3/}
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