The following properties of C[0,1] are proved here. Let T: C[0,1] → Y be a disjointness preserving bijection onto an arbitrary vector lattice Y. Then the inverse operator is also disjointness preserving, the operator T is regular, and the vector lattice Y is order isomorphic to C[0,1]. In particular if Y is a normed lattice, then T is also automatically norm continuous. A major step needed for proving these properties is provided by Theorem 3.1 asserting that T satisfies some technical condition that is crucial in the study of operators preserving disjointness.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-3-1,
author = {Y. A. Abramovich and A. K. Kitover},
title = {The Banach lattice C[0,1] is super d-rigid},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {337-355},
zbl = {1067.47050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-3-1}
}
Y. A. Abramovich; A. K. Kitover. The Banach lattice C[0,1] is super d-rigid. Studia Mathematica, Tome 157 (2003) pp. 337-355. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-3-1/