The Banach lattice C[0,1] is super d-rigid

Y. A. Abramovich, and A. K. Kitover. "The Banach lattice C[0,1] is super d-rigid." Studia Mathematica 159.3 (2003): 337-355. <http://eudml.org/doc/285076>.

@article{Y2003,
abstract = {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 $T^\{-1\}$ 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.},
author = {Y. A. Abramovich, A. K. Kitover},
journal = {Studia Mathematica},
keywords = {disjointness preserving; regular; vector lattice; -rigidity},
language = {eng},
number = {3},
pages = {337-355},
title = {The Banach lattice C[0,1] is super d-rigid},
url = {http://eudml.org/doc/285076},
volume = {159},
year = {2003},
}

TY - JOUR
AU - Y. A. Abramovich
AU - A. K. Kitover
TI - The Banach lattice C[0,1] is super d-rigid
JO - Studia Mathematica
PY - 2003
VL - 159
IS - 3
SP - 337
EP - 355
AB - 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 $T^{-1}$ 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.
LA - eng
KW - disjointness preserving; regular; vector lattice; -rigidity
UR - http://eudml.org/doc/285076
ER -