Let AI, be commutative semlslmple Banach algebras and 1 02 A2 be their projective tensor product. We prove that, if 10 2 is a group algebra (measure algebra) of a locally compact abelian group, then so are A 1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutatlve semi-simple Banach algebra, then the Banach algebra LI(G,A) of A-valued Bochner inte...

For a locally quasi-convex topological abelian group (G, τ), we study the poset C (G, τ) of all locally quasi-convex topologies on G that are compatible with τ (i.e., have the same dual as (G, τ)) ordered by inclusion. Obviously, this poset has always a bottom element, namely the weak topology σ(G, Ĝ). Whether it has also a top element is an open question. We study both quantitative aspects of ...

In response to a question raised by Halmos in his book on ergodic theory ([10], page 29) it was proved that a locally compact group admits a (bicontinuous) group automorphism acting ergodically (with respect to the Haar measure as a quasiinvariant measure) only if it is compact (see [9] for historical details and a generalisation to affine transformations; see [5] for the case of Lie groups). A...