The strong dual of measure algebras with certain locally convex topologies

The Strong Dual Of Measure Algebras With Certain Locally Convex Topologies

Hossein Javanshiri

• Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran

Rasoul Nasr-Isfahani

• Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran

• School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box: 19395-5746, Tehran, Iran

Abstract

For a locally compact group G, we introduce and study a class of locally convex topologies τ on the measure algebra M(G) of G. In particular, we show that the strong dual of (M(G),τ) can be identified with a closed subspace of the Banach space M(G)∗; we also investigate some properties of the locally convex space (M(G),τ).

Keywords: measure algebra; strict topology; locally compact group; locally convex space.

MSC: primary 43A10; secondary 43A15; 46A03; 46H05.