Hilbert modules over locally C*-algebras

Abstract

In the present paper the notion of a Hilbert module over a locally C*-algebra is discussed and some results are obtained on this matter. In particular, we give a detailed proof of the known result that the set of adjointable endomorphisms of such modules is itself a locally C*-algebra.

16 pages, LaTeX, essential references added

References in corpus (1)

• Hilbert C*-modules and related subjects - a guided reference overview I

Cited by in corpus (15)

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• Generic properties of module maps and characterizing inverse limits of C*-algebras of compact operators
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• Representations of *-semigroups associated to invariant kernels with values continuously adjointable operators
• Completely Positive Maps: Pro-C*-algebras and Hilbert modules over Pro-C*-algebras
• Induced representations of Hilbert modules over locally C*-algebras and the imprimitivity theorem
• On Hilbert modules over locally C*-algebras II
• On multipliers of Hilbert modules over locally C*-algebras
• Crossed products of locally C*-algebras and Morita equivalence
• Dilations on locally Hilbert spaces
• Crossed products by Hilbert pro-C*-bimodules versus tensor products
• Automatic Boundedness of Adjointable Operators on Barreled VH-Spaces
• Completely positive maps on Hilbert modules over pro-C*-algebras
• Some remarks on derivations on the algebra of operators in Hilbert pro-C*-bimodules
• On Morita equivalence of group actions on locally C*-algebras