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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

### Tom 159 / 2003

Studia Mathematica 159 (2003), 337-355 MSC: Primary 47B60. DOI: 10.4064/sm159-3-1

#### Streszczenie

The following properties of $C[0,1]$ are proved here. Let $T:C[0,1] \to Y$ 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.

#### Autorzy

• Y. A. AbramovichDepartment of Mathematical Sciences
IUPUI
Indianapolis, IN 46202, U.S.A.
• A. K. KitoverDepartment of Mathematics