In this paper, we will prove that if A is a C-algebra with an effective coaction ǫ by a compact quantum group, then the fixed point algebra and the reduced crossed product are Morita equivalent. As an application, we prove an imprimitivity type theorem for crossed products of coactions by discrete Kac C-algebras.

In this paper, we will give a natural definition for morphisms between multiplicative unitaries. We will then discuss some equivalences of this definition and some interesting properties of them. Moreover, we will define normal sub-multiplicative unitaries for multiplicative unitaries of discrete type and prove an imprimitivity type theorem for discrete multiplicative unitaries.

let $mathcal{a}$ be a banach algebra and $mathcal{m}$ be a banach $mathcal{a}$-bimodule. we say that a linear mapping $delta:mathcal{a} rightarrow mathcal{m}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{a} rightarrow mathcal{m}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{a}$. giving some facts concerning general...

Amenability is a cohomological property of Banach algebras which was introduced by Johnson in [14]. Let A be a Banach algebra, and suppose that X is a Banach A−bimodule such that the following statements hold ∥a · x∥ ≤ ∥a∥∥x∥ and ∥x · a∥ ≤ ∥a∥∥x∥ for each a ∈ A and x ∈ X. We can define the right and left actions of A on dual space X∗ of X via ⟨x, λ · a⟩ = ⟨a · x, λ⟩ ⟨x, a · λ⟩ = ⟨x · a, λ⟩, for...

We introduce the concept of reflexivity for bounded n-linear maps and investigate the reflexivity of Zn(L1(G),X), the space of bounded ncocycles from L1(G)(n) into X, where L1(G) is the group algebra of a locally compact group G and X is a Banach L1(G)-bimodule. We show that Zn(L1(G), X) is reflexive for a large class of groups including groups with polynomial growth, IN-groups, maximally almos...