We show that the unit ball of a full Hilbert C∗-module is sequentially compact in a certain weak topology if and only if the underlying C∗-algebra is finite dimensional. This provides an answer to the question posed in J. Chmieliński et al [Perturbation of the Wigner equation in inner product C∗-modules, J. Math. Phys. 49 (2008), no. 3, 033519].

The Morita equivalence of m-regular involutive quantales in the context of the theory of Hilbert A-modules is presented. The corresponding fundamental representation theorems are shown. We also prove that two commutative m-regular involutive quantales are Morita equivalent if and only if they are isomorphic. In the paper [5] F. Borceux and E.M. Vitale made a first step in extending the theory o...

Dosiev (2008) obtained a Stinespring’s theorem for local completely positive maps (in short: CP-maps) on locally C ∗ -algebras. In this article suitable notion of minimality construction has been identified so as to ensure uniqueness up unitary equivalence the associated representation. Using Radon–Nikodym type proved. Further, unbounded operator valued Hilbert modules over -algebras (also call...

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 C∗−algebraic framework. More particularly, we make use of the universal, or maximal, C∗−algebra generated by an operator algebra, and C∗−dilations. This technolog...

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...

We analzye Rieffel’s construction of generalized fixed point algebras in the setting of group actions on Hilbert modules. Let G be a locally compact group acting on a C∗-algebra B. We construct a Hilbert module F over the reduced crossed product of G and B, using a pair (E, R), where E is an equivariant Hilbert module over B and R is a dense subspace of E with certain properties. The generalize...