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On the second conjugate of the weighted semigroup algebra for a locally compact semigroup

On the second conjugate of the weighted semigroupalgebra for a locally compact 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 topological semigroup, ω be a weight function on S, and M a (S, ω) be the weightedsemigroup algebra of S. Let   (S; M a (S, ω)) be the C *-algebra of all M a (S, ω)-measurable functions g on S such that g/ω vanishes at infinity. Here, we consider   (S; M a (S, ω))* as a closed subalgebra of M a (S, ω)** equipped with the first Arens product, and study the relation between these two algebras. In particular, we show that   (S; M a (S, ω))* is a closed ideal ofM a (S, ω)** only when S is compact.

Keywords: Arens multiplication,  foundation semigroup,  second dual,weighted semigroup algebra

MSC: Primary 43A10, 43A20, Secondary 43A15, 46H05

 

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