It is known that a continuous family of compact operators can be diagonalized pointwise. One can consider this fact as a possibility of di-agonalization of the compact operators in Hilbert modules over a com-mutative W *-algebra. The aim of the present paper is to generalize this fact for a finite W *-algebra A not necessarily commutative. We prove that for a compact operator K acting in the ri...

With every (strict or normal) unital endomorphism of the algebra of all adjointable operators on a Hilbert module there is associated a correspondence (that is, a Hilbert bimodule) such that the endomorphism can be recovered as amplification of the identity representation with that correspondence. In these notes we show the converse of this statement in the case of strongly full W–correspondenc...

In this paper we introduce the curvature of densely defined universal connections on Hilbert C⁎-modules relative to a spectral triple (or unbounded Kasparov module), obtaining well-defined operator. Fixing triple, find that modulo junk forms, only depends represented form connection. We refine our definition factorizations modules. Our recovers all data Riemannian submersion compact manifolds, ...

For differential operators which are invariant under the action of an abelian group Bloch theory is the tool of choice to analyze spectral properties. By shedding some new non-commutative light on this we motivate the introduction of a noncommutative Bloch theory for elliptic operators on Hilbert C-modules. It relates properties of C-algebras to spectral properties of module operators such as b...

Given a locally compact abelian group $G$ and closed subgroup $\Lambda$ in $G\times\widehat{G}$, Rieffel associated to Hilbert $C^*$-module $\mathcal{E}$, known as Heisenberg module. He proved that $\mathcal{E}$ is an equivalence bimodule between the twisted $C^*$-algebra $C^*(\Lambda,\textsf{c})$ $C^*(\Lambda^\circ,\bar{\textsf{c}})$, where $\Lambda^{\circ}$ denotes adjoint of $\Lambda$. Our m...

In this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of Hilbert $C^ast-$ modules and vice versa, then we consider tensor products of g-Bessel multipliers, Bessel multipliers and Bessel fusion multipliers in Hilbert $C^ast-$modules. Moreover, we obtain so...