Displaying similar documents to “On quasi-free Hilbert modules.”

Normal Hilbert modules over the ball algebra A(B)

Kunyu Guo (1999)

Studia Mathematica

Similarity:

The normal cohomology functor E x t ℵ 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 E x t ℵ -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...

On full Hilbert C * -modules.

Moslehian, Mohammad Sal (2001)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Similarity:

On unitary equivalence of quasi-free Hilbert modules

Li Chen (2009)

Studia Mathematica

Similarity:

We characterize unitary equivalence of quasi-free Hilbert modules, which complements Douglas and Misra's earlier work [New York J. Math. 11 (2005)]. We first confine our arguments to the classical setting of reproducing Hilbert spaces and then relate our result to equivalence of Hermitian vector bundles.

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]

Similarity:

On a generalization of W*-modules

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

Banach Center Publications

Similarity:

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.

Projectivity and lifting of Hilbert module maps

Douglas N. Clark (1997)

Annales Polonici Mathematici

Similarity:

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.

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

Maria Joiţa (2011)

Open Mathematics

Similarity:

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.

A Morita equivalence for Hilbert C*-modules

Maria Joiţa, Mohammad Sal Moslehian (2012)

Studia Mathematica

Similarity:

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.

Tensor products of Hilbert modules over locally C * -algebras

Maria Joiţa (2004)

Czechoslovak Mathematical Journal

Similarity:

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.

Spectral and homological properties of Hilbert modules over the disc algebra

Raphaël Clouâtre (2014)

Studia Mathematica

Similarity:

We study general Hilbert modules over the disc algebra and exhibit necessary spectral conditions for the vanishing of certain associated extension groups. In particular, this sheds some light on the problem of identifying the projective Hilbert modules. Part of our work also addresses the classical derivation problem.