In the present paper we give a self-contained proof of Imprimitivity theorem for systems of covariance, or generalised imprimitivity systems, based on transitive spaces. The theorem holds for locally compact groups and non-normalised positive operator valued (POV) measures. For projective valued measures, the theorem was proven by Mackey, [21], for separable groups, and by Blattner, [4], in ful...

We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that it becomes induced by a Hilbert C(X)-bimodule. Furthermore we introduce the notion of C(X)-category, and discuss relationships with crossed products and duality for compact groups.

Let G be a locally compact group and π : G → U(H) a unitary representation of G. A commutative subalgebra of B(H) is called π-inductive when it is stable through conjugation by every operator in the range of π. This concept generalizes Mackey’s definition of a system of imprimitivity for π; it is expected that studying inductive algebras will lead to progress in the classification of realizatio...

Assume that $A$‎, ‎$B$ are Banach algebras and that $m:Atimes Brightarrow B$‎, ‎$m^prime:Atimes Arightarrow B$ are bounded bilinear mappings‎. ‎We study the relationships between Arens regularity of $m$‎, ‎$m^prime$ and the Banach algebras $A$‎, ‎$B$‎. ‎For a Banach $A‎$‎-bimodule $B$‎, ‎we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**}‎$‎-module‎. ‎Le...

Abstract We prove that the generator of $$L^2$$ L 2 implementation a KMS-symmetric quantum Markov semigroup can be expressed as square derivation with values in Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups seco...

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...

Watts’s Theorem says that a right exact functor F : ModR → ModS that commutes with direct sums is isomorphic to − ⊗R B where B is the R-S-bimodule FR. The main result in this paper is the following: if A is a cocomplete category and F : ModR→ A is a right exact functor commuting with direct sums, then F is isomorphic to − ⊗R F where F is a suitable R-module in A, i.e., a pair (F , ρ) consisting...

assume that $a$‎, ‎$b$ are banach algebras and that $m:atimes brightarrow b$‎, ‎$m^prime:atimes arightarrow b$ are bounded bilinear mappings‎. ‎we study the relationships between arens regularity of $m$‎, ‎$m^prime$ and the banach algebras $a$‎, ‎$b$‎. ‎for a banach $a‎$‎-bimodule $b$‎, ‎we show that $b$ factors with respect to $a$ if and only if $b^{**}$ is unital as an $a^{**}‎$‎-module‎. ‎le...

Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers η0 < η1 < η2 < · · · < η6 so that for every bounded, normal D-bimodule map Φ on B(H), either ‖Φ‖ > η6 or ‖Φ‖ = ηk for some k ∈ {0, 1, 2, 3, 4, 5, 6}. When D is totally atomic, these maps are the idempotent Schur multipliers and we characterise those with norm ηk for 0 ≤ k ≤ 6. We also show that the Schur idempote...