L-1 representation of Riesz spaces

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Turan B.

STUDIA MATHEMATICA, vol.176, no.1, pp.61-68, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 176 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.4064/sm176-1-4
  • Journal Name: STUDIA MATHEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.61-68
  • Gazi University Affiliated: Yes

Abstract

Let E be a Riesz space. By defining the spaces L-E(1) and L-E(infinity) of E, we prove that the center Z(L-E(1)) of L-E(1) is L-E(infinity) and show that the injectivity of the Arens homomorphism m: Z(E)" -> Z(E-similar to) is equivalent to the equality L-E(1) = Z(E)'. Finally, we also give some representation of an order continuous Banach lattice E with a weak unit and of the order dual E-similar to of E in L-E(1) which are different from the representations appearing in the literature.