The extensions of isometries between the 2-dimensional normed spaces

Abstract

Isometric operator is a very significant subject in the study of space structure. In this paper, we will give some results about the Tingley's problem, and give sufficient conditions for isometric operator $T_{0}$, which is between classical 2-dimensional normed sequence spaces such as $\ell^{(2)}_{p}$ and $\ell^{(2)}_{\infty}$, to have a linear extension in some way.