• SHOURIJEH, B. TABATABAIE (Department of Mathematics Shiraz University)
  • Received : 2004.02.26
  • Published : 2004.12.25


In this paper the left regular representation and the reduced $C^*$-algebra for a commutative separative semigroup is defined. The universal representation, the reduced $C^*$-algebra and the full $C^*$-algebra for the additive semigroup $N^+$ are given. Also it is proved that $C*_r(N^+){\ncong}C^*(N^+)$.


Left regular representation;cyclic representation;universal representation;reduced $C^*$-algebra and full $C^*$-algebra of a group


Supported by : Chungbuk National University


  1. Lectures on Operator theory Rajarama Bhat, B.V.;Elliott, George A.;Filmore, Peter A.(eds.)
  2. Fundamentals of the theory of Operator Algebras, Vol. I Kadison, R.V.;Ringrose, J.R.
  3. Fundamentals of the theory of Operator Algebras, advanced theory, vol. II Kadison, R.V.;Ringrose, J.R.
  4. C. R. Acad. Sci., Paris v.239 sur quelques proprietes de certaines classes de demi-groupes Thierrin, G.
  5. Kodai Math. Sem. Rep. On decompositions ofa commutative semigroup Tamura, T.;Kimura, N.
  6. A Hilbert space problem book Halmos, P.R.
  7. J. Math. Mech. v.19 Powers of partial isometries Halmos, P.R.;Wallen, L.J.
  8. Trans. Amer. Math. Soc. v.83 The ${\ell}^1$-algebra of a commutative semigroup Hewitt, E.;Zuckerman, H.
  9. Illinois J. Math. v.1 Amenable semigroups Day, M.M.
  10. Representations of Commutative semitopological semigroups;Lecture Notes in Maths Dunkl, C.F.;Ramirez, D.E.
  11. Math. Surveys no.7 The algebraic theory of semigroups, Vol. I Clifford, A.H.;Preston, G.B.
  12. TEX>$C^*$-Algebras by Example Davidson, Kenneth R.