On multipliers of Segal algebras

Abstract

Abstract. Let T be a multiplier of a Segal algebra S on a locally compact abelian group G. We prove that T2(S) is closed if and only if T is a product of an idempotent and an invertible multiplier. We also show that the techniques developed in the proof of this theorem can be used to obtain some other known results.

Compactness and Almost Periodicity of Multipliers

“…These facts generalize many of the results appearing in the literature (e.g. [2], [4], [7], [8]), and they all are a consequence of the absence of l.a.p. or l.w.a.p.…”

Multipliers with Closed Range on Regular Commutative Banach Algebras

“…Another interesting special case of Theorem 4.2 arises when 7 G M (A) is injective. We present here a new proof of a result, first noted for Tauberian algebras by Ransford, which in turn was a generalization of the same result for isometric multipliers on Tauberian regular algebras, noted by several authors, e.g., [DT,Theorem 2;ELN,Proposition 8]. Proof.…”

On compact multipliers of Banach algebras

“…(T is a multiplier of B if T is a linear operator satisfying T(fg) = / • Tg for /, g G B.) In this note we show that the regularity conditions used in [1] and [2] are unnecessary. SpecificaUy we prove the following.…”

“…In [1] and [2] it was shown that if a commutative semisimple Banach algebra B satisfies certain regularity conditions and if the maximal ideal space of B contains no isolated points, then every compact multiplier of B is trivial. (T is a multiplier of B if T is a linear operator satisfying T(fg) = / • Tg for /, g G B.)…”