The Strong Dual of Measure Algebras With Certain Locally Convex Topologies

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).2010 Mathematics subject classification: primary 43A10; secondary 43A15, 46A03, 46H05.

Introverted subspaces of the duals of measure algebras

“…We commence this section by recalling the main object of the work which is introduced and studied by the authors in [10].…”

“…Recently in the works [6,10], we studied the first and second duals of measure algebras by the use of the theory of generalised functions which have been introduced and investigated by Sre ȋdr [14] and Wong [15,16]. In those papers we observed that GL 0 (G), the space of all generalised functions that vanishes at infinity, plays a crucial role in our investigation.…”