Banach-stone theorem for Banach lattice valued continuous functions


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Ercan Z., Onal S.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.135, ss.2827-2829, 2007 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 135 Konu: 9
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1090/s0002-9939-07-08788-6
  • Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.2827-2829

Özet

Let Chi and Upsilon be compact Hausdor spaces, Epsilon be a Banach lattice and F be an AM space with unit. Let pi : C(X, E) -> C(Upsilon, F) be a Riesz isomorphism such that 0 not subset of f (X) if and only if 0 not subset of pi (f)(Upsilon) for each f is an element of C(Chi, Epsilon). We prove that Chi is homeomorphic to Upsilon and Epsilon is Riesz isomorphic to F. This generalizes some known results.