algebraic frames are generalizations of fourier transforms on locally compact abelian groups in the sense that the family of vectors forming the frame are replaced by a family of unbounded linear functionals. the paper studies the indexing measure space of the algebraic frames; as the investigation narrows down to the class of lower semiframes, more relations are revealed between the discret...

in his paper mentioned in the title, which appears in the same issue of this journal, mehdi radjabalipour derives the cyclic decomposition of an algebraic linear transformation. a more general structure theory for linear transformations appears in irving kaplansky's lovely 1954 book on infinite abelian groups. we present a translation of kaplansky's results for abelian groups into the...

Abstract. We study weak mixing of all orders for asymptotically abelian weakly mixing state preserving C*-dynamical systems, where the dynamics is given by the action of an abelian second countable locally compact group which contains a Følner sequence satisfying the Tempelman condition. For a smaller class of groups (which include Z and R) this is then used to show that an asymptotically abeli...

It is shown that a free topological group on a k.space is a k.-space. Using this it is proved that if X is a k.-group then it is a quotient of a free topological group by a free topological group. A corollary to this is that the projective dimension of any k.-group, relative to the class of all continuous epimorphisms admitting sections, is either zero or one. In particular the projective dimen...

Let A be an exact C–algebra, let G be a locally compact group, and let (A, G, α) be a C–dynamical system. Each automorphism αg induces a spatial automorphism Adλg on the reduced crossed product A×α G. In this paper we examine the question, first raised by E. Størmer, of when the topological entropies of αg and Adλg coincide. This had been answered by N. Brown for the particular case of discrete...

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

The Lie algebra of a nuclear group is a locally convex nuclear vector space. Mathematics Subject Classification (2000): 22B05, 22E65, 46Axx 1. The Lie Algebra of Abelian Topological Groups Let G be an abelian topological group. The set of all one–parameter–subgroups L(G) := {λ : R→ G : λ is a continuous homomorphism} is called the Lie algebra of G . We define addition pointwise and scalar multi...