We introduce the B-spline interpolation problem corresponding to a C∗-valued sesquilinear form on Hilbert C∗-module and study its basic properties as well uniqueness of solution. first in case when is self-dual. Passing setting W∗-modules, we present our main result by characterizing spline for extended has Finally, solutions C∗-modules over C∗-ideals W∗-algebras are extensively discussed.

It is shown that the metric on union of sets X and Y defines a Hilbert $C^*$ -module over uniform Roe algebra space with fixed dX. A number examples such -modules are described.

We study actions of discrete groups on Hilbert C-modules induced from topological actions on compact Hausdorff spaces. We prove that amenable actions give rise to proper affine isometric actions, provided there is a quasiinvariant measure which is sufficiently close to being invariant in a certain sense. This provides conditions on non-amenability of actions. The notion of amenability of group ...

We investigate the generalized derivations and show that every generalized derivation on a simple Hilbert C∗-module either is closable or has a dense range. We also describe dynamical systems on a full Hilbert C∗-module M over a C∗-algebra A as a oneparameter group of unitaries on M and prove that if α : R → U(M) is a dynamical system, where U(M) denotes the set of all unitary operator on M, th...