### On full Hilbert $C*$-modules.

Moslehian, Mohammad Sal (2001)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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Moslehian, Mohammad Sal (2001)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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Manuilov, V.M. (1996)

Acta Mathematica Universitatis Comenianae. New Series

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Kunyu Guo (1999)

Studia Mathematica

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The normal cohomology functor $Ex{t}_{\aleph}$ is introduced from the category of all normal Hilbert modules over the ball algebra to the category of A(B)-modules. From the calculation of $Ex{t}_{\aleph}$-groups, we show that every normal C(∂B)-extension of a normal Hilbert module (viewed as a Hilbert module over A(B) is normal projective and normal injective. It follows that there is a natural isomorphism between Hom of normal Shilov modules and that of their quotient modules, which is a new lifting theorem of normal...

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

The New York Journal of Mathematics [electronic only]

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Marc Rieffel (1972)

Studia Mathematica

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David P. Blecher, Jon E. Kraus (2010)

Banach Center Publications

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a recent paper of the first author and Kashyap, a new class of Banach modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the Riesz representation theorem for Hilbert spaces), which in turn generalize Hilbert spaces. In the present paper, we describe these modules, giving some motivation, and we prove several new results about them.

Thom, Andreas (2011)

Theory and Applications of Categories [electronic only]

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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.

Maria Joiţa (2008)

Studia Mathematica

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We investigate the structure of the multiplier module of a Hilbert module over a pro-C*-algebra and the relationship between the set of all adjointable operators from a Hilbert A-module E to a Hilbert A-module F and the set of all adjointable operators from the multiplier module M(E) to M(F).

W. H. Schikhof (1971)

Compositio Mathematica

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Arveson, William (2004)

Documenta Mathematica

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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.

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.