Let A be a dual Banach algebra with predual A∗ and consider the following assertions: (A) A is Connes-amenable; (B) A has a normal, virtual diagonal; A∗ is an injective A-bimodule. For general A, all that is known is that (B) implies (A) whereas, for von Neumann algebras, (A), (B), and (C) are equivalent. We show that (C) always implies (B) whereas the converse is false. Furthermore, we investi...

Let ? be an open connected subset of the complex plane C and let T be a bounded linear operator on a Hilbert space H. For ? in ? let e the orthogonal projection onto the null-space of T-?I . We discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. A generalized Gram- Schmidt process is also given.

If H is a quasi-Hopf algebra and B is a right H-comodule algebra such that there exists v : H → B a morphism of right H-comodule algebras, we prove that there exists a left Hmodule algebra A such that B ≃ A#H . The main difference comparing to the Hopf case is that, from the multiplication of B, which is associative, we have to obtain the multiplication of A, which in general is not; for this w...

We characterize the derivation d : A→ ΩDer(A) by a universal property introducing a new class of bimodules. Abridged English Version In this Note, A denotes an associative algebra over K = R or C with a unit 1l. In the Note [5], a graded differential algebra ΩDer(A) with Ω 0 Der(A) = A was introduced with the notation ΩD(A). It is one of the aims of this Note to show that, by introducing a new ...

We construct relativistic quantum Markov semigroups from covariant completely positive maps. proceed by generalizing a step in Stinespring's dilation to general system of imprimitivity and basing it on Poincare group. The resulting noise channels are relativistically consistent the method is applicable any fundamental particle, though we demonstrate for case light-like particles. Krauss decompo...

Let A and B be two Banach algebras and let M be a Banach B-bimodule. Suppose that σ : A → B is a linear mapping and d : A → M is a σ-derivation. We prove several results about automatic continuity of σderivations on Banach algebras. In addition, we define a notion for m-weakly continuous linear mapping and show that, under certain conditions, d and σ are m-weakly continuous. Moreover, we prove ...

Definition 3. Let B be a ring. Then, we denote by B [[t]] the ring of formal power series over B in the indeterminate t, where t is supposed to commute with every element of B. Formally, this means that we define B [[t]] as the ring of all sequences (b0, b1, b2, ...) ∈ BN (where N means the set {0, 1, 2, ...}), with addition defined by (b0, b1, b2, ...) + (b ′ 0, b ′ 1, b ′ 2, ...) = (b0 + b ′ ...

In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are  generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.

We give a sufficient condition for a bi-invariant weight on a Frobenius bimodule to satisfy the extension property. This condition applies to bi-invariant weights on a finite Frobenius ring as a special case. The complex-valued functions on a Frobenius bimodule are viewed as a module over the semigroup ring of the multiplicative semigroup of the coefficient ring.