### 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 |
---|---|

Pages (from-to) | 301-310 |

Number of pages | 10 |

Journal | Archiv der Mathematik |

Volume | 71 |

Issue number | 4 |

Publication status | Published - Oct 2 1998 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Archiv der Mathematik*,

*71*(4), 301-310.

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

Research output: Contribution to journal › Article

*Archiv der Mathematik*, vol. 71, no. 4, pp. 301-310.

}

TY - JOUR

T1 - Diameter preserving linear bijections of C(X)

AU - Györy, Máté

AU - Molnár, L.

PY - 1998/10/2

Y1 - 1998/10/2

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0032222016&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032222016

VL - 71

SP - 301

EP - 310

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

IS - 4

ER -