Diameter preserving linear bijections of C(X)

Máté Györy, L. Molnár

Research output: Article

27 Citations (Scopus)

Abstract

The aim of this paper is to solve a linear preserver problem on the function algebra C(X). We show that in the case in which 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 functional.

Original languageEnglish
Pages (from-to)301-310
Number of pages10
JournalArchiv der Mathematik
Volume71
Issue number4
Publication statusPublished - okt. 2 1998

Fingerprint

Linear Preserver
First Countable
Function Algebra
Compact Hausdorff Space
Linear Functional
Homeomorphism
Bijection
Form

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Diameter preserving linear bijections of C(X). / Györy, Máté; Molnár, L.

In: Archiv der Mathematik, Vol. 71, No. 4, 02.10.1998, p. 301-310.

Research output: Article

Györy, Máté ; Molnár, L. / Diameter preserving linear bijections of C(X). In: Archiv der Mathematik. 1998 ; Vol. 71, No. 4. pp. 301-310.
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