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

Michael Frank

doi:10.1017/is008001031jkt035

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

Operator Algebras 2025-04-29 v1 Functional Analysis

Authors: 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.

Keywords

c*-algebras of compact operators hilbert c*-modules orthogonal summand categorical properties biorthogonal complement norm-closed submodule

Cite

@article{arxiv.math/0611348,
  title  = {Characterizing C*-algebras of compact operators by generic categorical properties of Hilbert C*-modules},
  author = {Michael Frank},
  journal= {arXiv preprint arXiv:math/0611348},
  year   = {2025}
}

Comments

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