A fixed point approach to the stability of -morphisms on Hilbert -modules.
A Morita equivalence for Hilbert C*-modules
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.
A new proof for the multiplicative property of the boolean cumulants with applications to the operator-valued case
The paper presents several combinatorial properties of the boolean cumulants. A consequence is a new proof of the multiplicative property of the boolean cumulant series that can be easily adapted to the case of boolean independence with amalgamation over an algebra.
A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras.
Adding tails to -correspondences.
Additive functional inequalities in Banach modules.
Banach-Saks properties of C*-algebras and Hilbert C*-modules.
Bessel and Grüss type inequalities in inner product modules over Banach -algebras.
Bounded elements and spectrum in Banach quasi *-algebras
A normal Banach quasi *-algebra (,) has a distinguished Banach *-algebra 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 ().
Characterization of the order relation on the set of completely -positive linear maps between -algebras.
Commutants of von Neumann correspondences and duality of Eilenberg-Watts theorems by Rieffel and by Blecher
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...
Completely multi-positive linear maps between locally C*-algebras and representations on Hilbert modules
A KSGNS (Kasparov, Stinespring, Gel'fand, Naimark, Segal) type construction for strict (respectively, covariant non-degenerate) completely multi-positive linear maps between locally C*-algebras is described.
Continuous -frame in Hilbert -modules.
Covariant version of the Stinespring type theorem for Hilbert C*-modules
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
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.
-semigroups for continuous product systems: the nonunital case.
Equivalence bundles over a finite group and strong Morita equivalence for unital inclusions of unital -algebras
Let and be -algebraic bundles over a finite group . Let and . Also, let and , where is the unit element in . We suppose that and are unital and and have the unit elements in and , respectively. In this paper, we show that if there is an equivalence -bundle over with some properties, then the unital inclusions of unital -algebras and induced by and are strongly Morita equivalent. Also, we suppose that and are saturated and that . We show that if and ...
Errata on: “Banach-Saks properties of -algebras and Hilbert -modules”.
Finite generation in C*-algebras and Hilbert C*-modules
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.
Finite-dimensional Hilbert -modules.