Archiv der Mathematik

, Volume 71, Issue 4, pp 301–310

Diameter preserving linear bijections of C(X)

  • Máté Gyory
  • Lajos Molnár

DOI: 10.1007/s000130050268

Cite this article as:
Gyory, M. & Molnár, L. Arch. Math. (1998) 71: 301. doi:10.1007/s000130050268

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 \(\phi :C(X)\to C(X)\) having the property that \(\hbox {diam} (\phi (f)(X))=\hbox {diam} (f(X)) (f\in C(X))\) is of the form¶¶\( \phi (f)=\tau \cdot f\circ \varphi +t(f)1 \,\, (f\in C(X))\)¶¶where \(\tau \in {\Bbb C}, |\tau |=1, $\varphi :X\to X\) is a homeomorphism and \(t:C(X)\to {\Bbb C}\) is a linear functional.

Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • Máté Gyory
    • 1
  • Lajos Molnár
    • 1
  1. 1.Institute of Mathematics, Lajos Kossuth University, P.O. Box 12, HU-4010 Debrecen, HungaryHU