1997/07/04 by Máté Győry, M. Gyory, Gyory, M. +3
Mathematics · #46J10 #47B38 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Rings, Modules, and Algebras #math.FA #msc:46J10 #msc:47B38
paper · pdf · doi:10.48550/arxiv.math/9707208
arxiv created 1997/07/04 · openalex publication_date 1997/07/04 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 is a complex number of modulus 1, φ:X→ X is a homeomorphism and t is a linear functional on C(X).