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

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

2006-11-12

arxiv.org/abs/math/0611348v1

Mathematics

Operator Algebras

9 pages, part of a collection dedicated to the memory of Yu. P. Solovyov (Moscow State University). to appear in K-Theory

Scientific paper

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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