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].