Multipliers of Segal Algebras

Abstract

This thesis studies multipliers on some of the Segal Algebras, and characterises various spaces of multipliers. Analogous results are obtained. The thesis yields characterisation of the multiplier spaces on the Segal Algebras. Biopositive and isometric isomorphisms of multiplier algebras are discussed. In particular it is proved that for two groups G1 and G2, a biopositive isomorphism, of the multiplier spaces of the Segal algebras induces a topological isomorphism between G1 and G2. The problem of restriction of a multiplier to a subset of a dual space is also discussed. Larson's question as to "whether there exist non-zero closed translation invariant subspaces..." was discussed and answered in the last chapter.