Displaying similar documents to “A Duality Between Hilbert Modules And Fields Of Hilbert Spaces.”

A Morita equivalence for Hilbert C*-modules

Maria Joiţa, Mohammad Sal Moslehian (2012)

Studia Mathematica

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We introduce a notion of Morita equivalence for Hilbert C*-modules in terms of the Morita equivalence of the algebras of compact operators on Hilbert C*-modules. We investigate the properties of the new Morita equivalence. We apply our results to study continuous actions of locally compact groups on full Hilbert C*-modules. We also present an extension of Green's theorem in the context of Hilbert C*-modules.

Projectivity and lifting of Hilbert module maps

Douglas N. Clark (1997)

Annales Polonici Mathematici

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In a recent paper, Carlson, Foiaş, Williams and the author proved that isometric Hilbert modules are projective in the category of Hilbert modules similar to contractive ones. In this paper, a simple proof, based on a strengthened lifting theorem, is given. The proof also applies to an equivalent theorem of Foiaş and Williams on similarity to a contraction of a certain 2 × 2 operator matrix.

Projective Hilbert A(D)-modules.

Carlson, Jon F., Clark, Douglas N., Foias, Ciprian, Williams, J.P. (1994)

The New York Journal of Mathematics [electronic only]

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Generalized n-circular projections on JB*-triples and Hilbert C0(Ω)-modules

Dijana Ilišević, Chih-Neng Liu, Ngai-Ching Wong (2017)

Concrete Operators

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Being expected as a Banach space substitute of the orthogonal projections on Hilbert spaces, generalized n-circular projections also extend the notion of generalized bicontractive projections on JB*-triples. In this paper, we study some geometric properties of JB*-triples related to them. In particular, we provide some structure theorems of generalized n-circular projections on an often mentioned special case of JB*-triples, i.e., Hilbert C*-modules over abelian C*-algebras C0(Ω). ...

Covariant version of the Stinespring type theorem for Hilbert C*-modules

Maria Joiţa (2011)

Open Mathematics

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In this paper, we prove a covariant version of the Stinespring theorem for Hilbert C*-modules. Also, we show that there is a bijective correspondence between operator valued completely positive maps, (u′, u)-covariant with respect to the dynamical system (G, η, X) on Hilbert C*-modules and (u′, u)-covariant operator valued completely positive maps on the crossed product G ×η X of X by η.

Tensor products of Hilbert modules over locally C * -algebras

Maria Joiţa (2004)

Czechoslovak Mathematical Journal

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In this paper the tensor products of Hilbert modules over locally C * -algebras are defined and their properties are studied. Thus we show that most of the basic properties of the tensor products of Hilbert C * -modules are also valid in the context of Hilbert modules over locally C * -algebras.