A note on nonlinear isometries between vector-valued function spaces

TL;DR

This paper explores the structure of surjective isometries between subspaces of vector-valued function spaces, extending understanding beyond linear transformations.

Contribution

It characterizes the general form of surjective (not necessarily linear) isometries between subspaces of vector-valued function spaces.

Findings

Identifies the structure of nonlinear isometries

Extends classical linear isometry results

Provides a framework for understanding isometries in vector-valued function spaces

Abstract

In this paper, we investigate the general form of surjective (not necessarily linear) isometries T : A-> B between subspaces A and B of C(X;E) and C(Y;F), respectively.