The Banach-Stone theorem revisited

ERCAN Z., ÖNAL S.

TOPOLOGY AND ITS APPLICATIONS, vol.155, no.16, pp.1800-1803, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 155 Issue: 16
  • Publication Date: 2008
  • Doi Number: 10.1016/j.topol.2008.05.018
  • Journal Name: TOPOLOGY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1800-1803
  • Middle East Technical University Affiliated: Yes

Abstract

Let X and Y be compact Hausclorff spaces, and E and F be locally solid Riesz spaces. If pi : C(X. E) -> C(Y, F) is a 1-biseparating Riesz isomorphism then X and Y are homeomorphic, and E and F are Riesz isomorphic. This generalizes the main results of [Z. Ercan, S. Onal, Banach-Stone theorem for Banach lattice valued continuous functions, Proc. Amer. Math. Soc. 135 (9) (2007) 2827-2829] and [X. Miao, C. Xinhe, H. Jiling, Banach-Stone theorems and Riesz algebras, J. Math. Anal. Appl. 313 (1) (2006) 177-183], and answers a conjecture in [Z. Ercan, S. Onal, Banach-Stone theorem for Banach lattice valued continuous functions. Proc. Amer. Math. Soc. 135 (9) (2007) 2827-2829]. (C) 2008 Elsevier B.V. All rights reserved.