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

2011/08/30 by Kamran Sharifi, Sharifi, Kamran · 1 citation
Mathematics · #15A09 #46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 46L08 #Secondary 47A05

paper · pdf · doi:10.48550/arxiv.1108.5826

openalex publication_date 2011/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Invariant submodules of modular operators and Lomonosov type theorem for Hilbert C*-modules

Related

• Injective and projective Hilbert C*-modules, and C*-algebras of compact operators
• On Hilbert modules over locally C*-algebras II
• On multipliers of Hilbert modules over locally C*-algebras
• Hilbert modules over locally C*-algebras
• The reflexive closure of the adjointable operators