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arXiv:math/0611348 [math.OA]AbstractReferencesReviewsResources

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

Michael Frank

Published 2006-11-12Version 1

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.

Comments: 9 pages, part of a collection dedicated to the memory of Yu. P. Solovyov (Moscow State University). to appear in K-Theory
Categories: math.OA, math.FA
Subjects: 46L08, 46H25
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