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

• Autorzy: Y. A. Abramovich , A. K. Kitover
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B60: Operators on ordered spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 159
• Numer: 3
• Strony: 337-355

Daty

wydano

2003

Twórcy

autor

Y. A. Abramovich

• Department of Mathematical Sciences, IUPUI, Indianapolis, IN 46202, U.S.A.

autor

A. K. Kitover

• Department of Mathematics, Community College of Philadelphia, 1700 Spring Garden Street, Philadelphia, PA 19130, U.S.A.

Identyfikatory

DOI

10.4064/sm159-3-1