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A Morita equivalence for Hilbert C*-modules

Maria Joiţa, Mohammad Sal Moslehian (2012)

Studia Mathematica

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.

Bounded elements and spectrum in Banach quasi *-algebras

Camillo Trapani (2006)

Studia Mathematica

A normal Banach quasi *-algebra (,) has a distinguished Banach *-algebra b consisting of bounded elements of . The latter *-algebra is shown to coincide with the set of elements of having finite spectral radius. If the family () of bounded invariant positive sesquilinear forms on contains sufficiently many elements then the Banach *-algebra of bounded elements can be characterized via a C*-seminorm defined by the elements of ().

Commutants of von Neumann correspondences and duality of Eilenberg-Watts theorems by Rieffel and by Blecher

Michael Skeide (2006)

Banach Center Publications

The category of von Neumann correspondences from 𝓑 to 𝓒 (or von Neumann 𝓑-𝓒-modules) is dual to the category of von Neumann correspondences from 𝓒' to 𝓑' via a functor that generalizes naturally the functor that sends a von Neumann algebra to its commutant and back. We show that under this duality, called commutant, Rieffel's Eilenberg-Watts theorem (on functors between the categories of representations of two von Neumann algebras) switches into Blecher's Eilenberg-Watts theorem (on functors...

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

Maria Joiţa (2011)

Open Mathematics

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.

Crossed products by Hilbert pro-C*-bimodules

Maria Joiţa, Ioannis Zarakas (2013)

Studia Mathematica

We define the crossed product of a pro-C*-algebra A by a Hilbert A-A pro-C*-bimodule and we show that it can be realized as an inverse limit of crossed products of C*-algebras by Hilbert C*-bimodules. We also prove that under some conditions the crossed products of two Hilbert pro-C*-bimodules over strongly Morita equivalent pro-C*-algebras are strongly Morita equivalent.

Equivalence bundles over a finite group and strong Morita equivalence for unital inclusions of unital C * -algebras

Kazunori Kodaka (2022)

Mathematica Bohemica

Let 𝒜 = { A t } t G and = { B t } t G be C * -algebraic bundles over a finite group G . Let C = t G A t and D = t G B t . Also, let A = A e and B = B e , where e is the unit element in G . We suppose that C and D are unital and A and B have the unit elements in C and D , respectively. In this paper, we show that if there is an equivalence 𝒜 - -bundle over G with some properties, then the unital inclusions of unital C * -algebras A C and B D induced by 𝒜 and are strongly Morita equivalent. Also, we suppose that 𝒜 and are saturated and that A ' C = 𝐂 1 . We show that if A C and B D ...

Finite generation in C*-algebras and Hilbert C*-modules

David P. Blecher, Tomasz Kania (2014)

Studia Mathematica

We characterize C*-algebras and C*-modules such that every maximal right ideal (resp. right submodule) is algebraically finitely generated. In particular, C*-algebras satisfy the Dales-Żelazko conjecture.

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