The Banach-Stone theorem revisited

2008-10-01
ERCAN, ZAFER
Önal, Süleyman
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].

Citation Formats
Z. ERCAN and S. Önal, “The Banach-Stone theorem revisited,” TOPOLOGY AND ITS APPLICATIONS, vol. 155, no. 16, pp. 1800–1803, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46879.