Generic properties of module maps and characterizing inverse limits of C*-algebras of compact operators

Abstract

We study closedness of the range, adjointability and generalized invertibility of modular operators between Hilbert modules over locally C*-algebras of coefficients. Our investigations and the recent results of M. Frank [Characterizing C*-algebras of compact operators by generic categorical properties of Hilbert C*-modules, {\it J. K-Theory} {\bf 2} (2008), 453-462] reveal a number of equivalence properties of the category of Hilbert modules over locally C*-algebras which characterize precisely the inverse limit of C*-algebras of the C*-algebra of compact operators.

11 pages, accepted

References in corpus (4)

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

Cited by in corpus (2)

• Induced representations of Hilbert modules over locally C*-algebras and the imprimitivity theorem
• Completely positive maps on Hilbert modules over pro-C*-algebras