Related papers: Weak frames in Hilbert C*-modules with application…

We show how the data of a finite dimensional weak C^*-Hopf algebra can be encoded into a pair (H,V) where H is a finite dimensional Hilbert space and V: H \o H --> H \o H is a partial isometry satisfying, among others, the pentagon…

In the 1970s Alain Connes identified the appropriate notion of amenabilty for von Neumann algebras, and used it to obtain a deep internal finite dimensional approximation structure for these algebras. This structure is exactly what is…

Let (G,P) be a quasi-lattice ordered group and let X be a compactly aligned product system over P of Hilbert bimodules. Under mild hypotheses we associate to X a C*-algebra which we call the Cuntz-Nica-Pimsner algebra of X. Our construction…

In his seminal paper "Generalized Fixed Point Algebras and Square-Integrable Group Actions", Ralf Meyer showed how to construct generalized fixed-point algebras for $ C^{\ast} $-dynamical systems via their square-integrable representations…

We define the class of weakly approximately divisible unital C*-algebras and show that this class is closed under direct sums, direct limits, any tensor product with any C*-algebra, and quotients. A nuclear C*-algebra is weakly…

A precise description of the injective envelope of a spatial continuous trace C*-algebra A over a Stonean space Delta is given. The description is based on the notion of a weakly continuous Hilbert bundle, which we show to be a…

We investigate complexes of Hilbert C*-modules, which are cochain complexes with (unbounded) regular operators between Hilbert C*-modules as differential maps. In particular, we provide various equivalent characterizations of the Fredholm…

In this paper we investigate a *-algebra $\cX$ of fractions associated with a unital complex *-algebra $\cA$. The algebra $\cX$ and its Hilbert space representations are used to prove abstract noncommutative strict Positivstellens\"atze for…

An abstract characterization of weakly monotone $C^*$-algebras, namely the concrete $C^*$-algebras generated by creators and annihilators acting on the so-called weakly monotone Fock spaces, is given in terms of (quotient of) suitable…

Let $\Lambda$ be a lattice in a second countable, locally compact abelian group $G$ with annihilator $\Lambda^{\perp} \subseteq \widehat{G}$. We investigate the validity of the following statement: For every $\eta$ in the Feichtinger…

We study the theory of a Hilbert space H as a module for a unital C*-algebra A from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are…

We give a construction of Gabor type frames for suitable separable subspaces of the non-separable Hilbert spaces $AP_2({\mathbb R})$ of almost periodic functions of one variable. Furthermore we determine a non-countable generalized frame…

Theory of extensions of Hilbert C*-modules was developed by D. Bakic and B. Guljas. An easy observation shows that in the case, when the underlying C*-algebra extension is commutative and the Hilbert C*-modules are projective of finite…

We introduce and study some new uniform structures for Hilbert $C^*$-modules over an algebra $A$. In particular, we prove that in some cases they have the same totally bounded sets. To define one of them, we introduce a new class of…

Given a compact space X and two commuting continuous open surjective maps sigma_1, sigma_2 : X --> X, we construct certain C*-algebras that reflect the dynamics of the N^2-action. When the maps sigma_1, sigma_2 are local homeomorphisms,…

We develop a theory of Hilbert $\widetilde{\C}$-modules by investigating their structural and functional analytic properties. Particular attention is given to finitely generated submodules, projection operators, representation theorems for…

We continue our study of the general theory of possibly nonselfadjoint algebras of operators on a Hilbert space, and modules over such algebras, developing a little more technology to connect `nonselfadjoint operator algebra' with the…

We prove, among other results, that three standard measures of weak non-compactness coincide in preduals of JBW$^*$-triples. This result is new even for preduals of von Neumann algebras. We further provide a characterization of…

In this paper, we introduce the notion of invariant submodule in the theory of Hilbert C*-modules and study some basic properties of bounded adjointable operators and their generalized inverses which have nontrivial invariant submodules. We…

We apply the theory of finite dimensional weak C^*-Hopf algebras A as developed by G. B\"ohm, F. Nill and K. Szlach\'anyi to study reducible inclusion triples of von-Neumann algebras N \subset M \subset (M\cros\A). Here M is an A-module…