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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| Vydáno v: | Indian journal of pure and applied mathematics Ročník 56; číslo 2; s. 728 - 736 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Heidelberg
Springer Nature B.V
01.06.2025
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| ISSN: | 0019-5588, 0975-7465 |
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| Abstract | 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). |
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| AbstractList | 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). |
| Author | An, Aimin Wang, Wenting |
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| Copyright | The Indian National Science Academy 2023. |
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| DOI | 10.1007/s13226-023-00514-y |
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| Snippet | 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... |
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| Title | On ε-phase-isometries between the positive cones of continuous function spaces |
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