The Aleksandrov problem and the Tingley problem for expansive and nonexpansive operators in p-normed spaces
Jian-Zhong Xiao, Zhu Feng-qin · Operators and Matrices · 2024
In this paper several positive answers are given to the Aleksandrov type problems and the Tingley type problems for some expansive and nonexpansive operators between a real pnormed space and a real q -normed space (0 < p,q 1) . On the basis of the characteristics of p -normed spaces, the notion of isometry is generalized to the case of with some parameters. It is obtained that some operators of distance preserving can become isometries, and some isometric operators can be extended from the unit sphere to the whole space.