Min-phase-isometries on the unit sphere of Lp-type spaces
Abstract
Let X,Y be two real Lp-spaces (p>0), then a surjective map f:SX->SY satisfies
min{||f(x)+f(y)||,||f(x)-f(y)||} = min{||x+y||,||x−y||} (x,y∈SX),
if and only if f is a multiplication of a linear isometry and a map with rang {−1,1}. It can be regarded as a new Wigner’s theorem for real Lp-spaces (p>0).
Copyright © 2024 Lu Yuan. 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
L. Yuan, Min-phase-isometries on the unit sphere of Lp-type spaces, Adv. Fixed Point Theory 14 (2024), 15. https://doi.org/10.28919/afpt/8523
BibTeX
@article{Yuan2024,
author = {Yuan, Lu},
title = {Min-phase-isometries on the unit sphere of Lp-type spaces},
journal = {Adv. Fixed Point Theory},
volume = {14},
year = {2024},
pages = {15},
doi = {10.28919/afpt/8523}
}