On ε-phase-isometries between the positive cones of continuous function spaces

Let K and T be compact Hausdorff spaces, C+(K)={f∈C(K):f(k)≥0forallk∈K} be the positive cone of C(K). In this paper, we prove that if K is a compact Hausdorff perfectly normal space, then for every ε-phase-isometry F:C+(K)→C+(T), there are nonempty closed subset S⊂T and an additive isometry V:C+(K)→...

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Veröffentlicht in:Indian journal of pure and applied mathematics Jg. 56; H. 2; S. 728 - 736
Hauptverfasser: Wang, Wenting, An, Aimin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Heidelberg Springer Nature B.V 01.06.2025
Schlagworte:
Banach spaces
Function space
Mathematical functions
Mathematicians
ISSN:0019-5588, 0975-7465
Online-Zugang:Volltext
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Zusammenfassung:Let K and T be compact Hausdorff spaces, C+(K)={f∈C(K):f(k)≥0forallk∈K} be the positive cone of C(K). In this paper, we prove that if K is a compact Hausdorff perfectly normal space, then for every ε-phase-isometry F:C+(K)→C+(T), there are nonempty closed subset S⊂T and an additive isometry V:C+(K)→C+(S) defined as V(f)=limn→∞F(2nf)|S2n for each f∈C+(K) satisfying that ‖F(f)|S-V(f)‖≤32ε,forallf∈C+(K).Moreover, if F is almost surjective, then there exists a unique homeomorphism γ:T→K such that |F(f)(t)-f(γ(t))|≤32ε,t∈T,f∈C+(K).
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-023-00514-y