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