Extension of phase-isometries between the unit spheres of complex lp(Γ)-spaces (p>1)
Jianan Yang, Lingen Zhu, Yarong Zhang
Abstract
Let Γ, ∆ be nonempty index sets. For p ∈ (1, ∞), we prove that every surjective mapping f: Slp(Γ) → Slp(∆) satisfying the functional equation
{||f(x) + f(y)||, ||f(x)− f(y)||} = {||x+y||, ||x−y||} (x, y ∈ Slp(Γ)),
its positive homogeneous extension is a phase-isometry which is phase equivalent a real linear isometry.
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Published: 2021-03-02
How to Cite this Article:
Jianan Yang, Lingen Zhu, Yarong Zhang, Extension of phase-isometries between the unit spheres of complex lp(Γ)-spaces (p>1),
Adv. Fixed Point Theory, 11 (2021), Article ID 4
Copyright © 2021 Jianan Yang, Lingen Zhu, Yarong Zhang. This is an open access article distributed under the
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Advances in Fixed Point Theory
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