Extension of phase-isometries between the unit spheres of complex lp(Γ)-spaces (p>1)
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.
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.
Cite this article
J. Yang, L. Zhu, Y. Zhang, Extension of phase-isometries between the unit spheres of complex lp(Γ)-spaces (p>1), Adv. Fixed Point Theory 11 (2021), 4. https://doi.org/10.28919/afpt/5324
BibTeX
@article{Yang2021,
author = {Yang, Jianan and Zhu, Lingen and Zhang, Yarong},
title = {Extension of phase-isometries between the unit spheres of complex lp(Γ)-spaces (p>1)},
journal = {Adv. Fixed Point Theory},
volume = {11},
year = {2021},
pages = {4},
doi = {10.28919/afpt/5324}
}