Compact right multipliers on a Banach algebra related to locally compact semigroups

Compact right multipliers on a Banach algebra related to locally compact semigroups

Saeid Maghsoudi

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

• Department of Mathematics, Zanjan University, Zanjan, Iran

Mohammad Javad Mehdipour

• Department of Mathematics, Shiraz University of Technology, Shiraz, 71555-313, Iran

Rasoul Nasr-Isfahani

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

• School of Mathematics, Institute for Research in Fundamental Science (IPM), Tehran, P.O. Box: 19395-5746, Iran

Abstract

For a locally compact semigroup S , let L∞0(S,Ma(S)) be the Banach space of all μ-measurable ( μ∈Ma(S) ) functions vanishing at infinity, where Ma(S) denotes the algebra of all measures in the measure algebra M(S) of S with continuous translations. Here, we study right compact multipliers on the Banach algebra L∞0(S,Ma(S))∗ equipped with an Arens product.