### 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 language | English |
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Pages (from-to) | 301-310 |

Number of pages | 10 |

Journal | Archiv der Mathematik |

Volume | 71 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 2 1998 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Györy, M., & Molnár, L. (1998). Diameter preserving linear bijections of C(X).

*Archiv der Mathematik*,*71*(4), 301-310. https://doi.org/10.1007/s000130050268