L-1 representation of Riesz spaces

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Turan B.

STUDIA MATHEMATICA, cilt.176, sa.1, ss.61-68, 2006 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 176 Sayı: 1
  • Basım Tarihi: 2006
  • Doi Numarası: 10.4064/sm176-1-4
  • Dergi Adı: STUDIA MATHEMATICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.61-68
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Gazi Üniversitesi Adresli: Evet

Özet

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.