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

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.

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

References in corpus (4)

• Frames in Hilbert C*-modules and C*-algebras
• Adjointability of densely defined closed operators and the Magajna-Schweizer Theorem
• Generalized inverses and polar decomposition of unbounded regular operators on Hilbert $C^{\ast }$-modules
• Injective and projective Hilbert C*-modules, and C*-algebras of compact operators

Cited by in corpus (15)

• Adjointability of densely defined closed operators and the Magajna-Schweizer Theorem
• Generalized inverses and polar decomposition of unbounded regular operators on Hilbert $C^{\ast }$-modules
• The product of operators with closed range in Hilbert C*-modules
• EP modular operators and their products
• Moore-Penrose inverse of Gram operator on Hilbert C*-modules
• Injective and projective Hilbert C*-modules, and C*-algebras of compact operators
• Generic properties of module maps and characterizing inverse limits of C*-algebras of compact operators
• Left multipliers of reproducing kernel Hilbert $C^{\ast }$-modules and the Papadakis theorem
• Realizing the braided Temperley-Lieb-Jones C*-tensor categories as Hilbert C*-modules
• Extensions of the Lax-Milgram theorem to Hilbert C*-modules
• Power-norms based on Hilbert $C^{\ast }$-modules
• Structure theory of homologically trivial and annihilator locally C*-algebras
• A characterization of Hilbert $C^{\ast }$-modules over finite dimensional $C^{\ast }$-algebras
• Isomorphisms and Automorphisms of Discrete Multiplier Hopf C*-algebras
• Some examples of EP operators