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On the topological center of a Banach algebra related to a foundation topological semigroup

On the topological center of a Banach algebra related to a foundation topological semigroup

 

Saeid Maghsoudi

  • Department of Mathematics, University of Zanjan, Zanjan, 45195-313, Iran

 

Rasoul Nasr-Isfahani

  • Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 841546-83111, Iran
  • School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box: 19395-5746, Tehran, Iran

 

Abstract

Let S be a locally compact semigroup and L∞0(S,Ma(S)) be the Banach space of all μ-measurable ( μMa(S) ) functions vanishing at infinity, where Ma(S) denotes the algebra of all measures with continuous translations. Recently, we have shown that L∞0(S,Ma(S))∗ can be equipped with an Arens type product. Here, we show that the topological center ofL∞0(S,Ma(S))∗ coincides with Ma(S) for a class of locally compact semigroups S : this gives a partial solution to a conjecture raised by the authors.

Keywords: Arens product, Locally compact semigroups, Topological center

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