In this paper an algebraic star product and differential one defined on a regular coadjoint orbit of a compact semisimple group are compared. It is proven that there is an injective algebra homomorphism between the algebra of polynomials with the algebraic star product and the algebra of differential functions with the differential star product structure. Investigation supported by the Universi...

Abstract. We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A1 and A2 are operator algebras, then any bounded epimorphism of A1 onto A2 is completely bounded provided that A2 contains a norming C ∗-subalgebra. We use this result to give some insights into Kadison’s Similarity Problem: we show that every faithful bounded homomo...

A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for some discrete space ?. We investigate ideal J*-algebras and show that the a...

For finitary set functors preserving inverse images several concepts of coalgebras A are proved to be equivalent: (i) A has a homomorphism into the initial algebra, (ii) A is recursive, i.e., A has a unique coalgebra-to-algebra morphism into any algebra, and (iii) A is parametrically recursive. And all these properties mean that the system described by A always halts in finitely many steps.

Let A be a unital amenable A∗-algebra, or a unital commutative hermitian Banach ∗-algebra. We show that if ρ : A → B(H) is a bounded homomorphism, then ρ is completely bounded and ‖ρ‖cb ≤ ‖ρ‖2. Mathematics Subject Classification: 46L07; 46k05

A topological space X is called A-real compact, if every algebra homomorphism from A to the reals is an evaluation at some point of X, where A is an algebra of continuous functions. Our main interest lies on algebras of smooth functions. In [AdR] it was shown that any separable Banach space is smoothly real compact. Here we generalize this result to a huge class of locally convex spaces includi...

Abstract We prove two theorems about the Malcev Lie algebra associated to Torelli group of a surface genus g : Stably, it is Koszul and kernel Johnson homomorphism consists only trivial $\mathrm {Sp}_{2g}(\mathbb {Z})$ -representations lying in centre.

For almost finite groupoids, we study how their homology groups reflect dynamical properties of their topological full groups. It is shown that two clopen subsets of the unit space has the same class in H0 if and only if there exists an element in the topological full group which maps one to the other. It is also shown that a natural homomorphism, called the index map, from the topological full...

Let G be a connected real Lie group. The universal representation kernel, Ko, oí G is defined as the intersection of all kernels of continuous finite dimensional representations of G. Evidently, Ko is a closed normal subgroup of G, and it is known from a theorem due to Goto (cf. [l, Theorem 7.1]) that G/Ko has a faithful continuous finite dimensional representation. Thus Kg is the smallest norm...