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• # Artykuł - szczegóły

## Studia Mathematica

2003 | 159 | 3 | 337-355

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

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.

337-355

wydano
2003

### Twórcy

autor
• Department of Mathematical Sciences, IUPUI, Indianapolis, IN 46202, U.S.A.
autor
• Department of Mathematics, Community College of Philadelphia, 1700 Spring Garden Street, Philadelphia, PA 19130, U.S.A.