Diameter preserving linear bijections of C ( X )
نویسندگان
چکیده
منابع مشابه
. FA ] 4 J ul 1 99 7 DIAMETER PRESERVING LINEAR BIJECTIONS OF C ( X )
The aim of this paper is to solve a linear preserver problem on the function algebra C(X). We show that in case X is a first countable compact Hausdorff space, every linear bijection φ : C(X) → C(X) having the property that diam(φ(f)(X)) = diam(f(X)) (f ∈ C(X)) is of the form φ(f) = τ · f ◦ φ+ t(f)1 (f ∈ C(X)) where τ ∈ C, |τ | = 1, φ : X → X is a homeomorphism and t : C(X) → C is a linear func...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 1998
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s000130050268