Irreducible Representations of Hilbert <i>C*</i>-Modules

Operator-valued maps on Hilbert C^∗-modules

“…The study of ϕ-maps on Hilbert C * -modules has increased significantly during recent decades. In this context, several concepts such as representation theory of Hilbert C * -modules, dilation theory of ϕ-maps and CP-extendable maps were studied ( [1,3,4,5,6,9,11,12,16,17]). Therefore it becomes natural to concentrate on ϕ-maps as important maps on Hilbert C * -modules.…”

Simulated Quenching for Cancellation of Non-Linear Multi-Antennas Coupling

“…Hence, two SQ methods evolved: standard SQ which focuses on precision and Improved Fast SQ where search progress is accelerated on the cost of the decoupling precision. In most practical cases the reasonable assumption for the coupling functions is to model them as polynomials and limit them to third order nonlinear behavior which is consistent with the analog electronic elements and follows the nonlinear behavior experienced in many radio frequency (RF) front ends [1]. Hence, if no direct distortion is present, the input of two AD converters can be described mathematically as:…”

On representations of Banach C*-modules associated with biweights

“…A representation of E is a map Π : E → L(H, K) with the property that there is a * -representation π of A on K such that Π (x) , Π (y) = π ( x, y ) for all x, y ∈ E (see, for example, [2]). If (π, Π) is a representation of the left Hilbert C * -module E, then Π is linear and Π (ax) = π (a) Π (x) for all a ∈ A and for all x ∈ E and so it is an operator representation of the left Banach C * -module E in the sense of Definition 5.1.…”

“…-algebra A is a left A-module equipped with an A-valued inner product and which is complete with respect to the topology induced by the inner product (see, for instance, [2] …”

“…Clearly any C * -algebra is a left Banach C * -module as well as any left Hilbert C * -module. In [2] Lj. Arambašić introduced the concept of nondegenerate, irreducible representation of a Hilbert C * -module.…”