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Characterizing C*-algebras of compact operators by generic categorical properties of Hilbert C*-modules

Michael Frank
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Abstract

B. Magajna and J. Schweizer showed in 1997 and 1999, respectively, that C*-algebras of compact operators can be characterized by the property that every norm-closed (and coinciding with its biorthogonal complement, resp.) submodule of every Hilbert C*-module over them is automatically an orthogonal summand. We find out further generic properties of the category of Hilbert C*-modules over C*-algebras which characterize precisely the C*-algebras of compact operators.

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Michael Frank. 2006-11-12. Characterizing C*-algebras of compact operators by generic categorical properties of Hilbert C*-modules. https://doi.org/10.1017/is008001031jkt035

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