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 Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

ISSN: 1927-6303

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