A representation of isometries on function spaces

TL;DR

This paper characterizes surjective isometries between ideal Banach function spaces as transformations involving measurable changes of variables and multiplication, providing a structural understanding of these symmetries.

Contribution

It offers a new representation theorem for isometries on ideal Banach function spaces, linking geometric transformations to measurable and multiplicative operations.

Findings

Surjective isometries can be expressed as composition with measurable transformations and multiplication.

The result applies to ideal Banach function spaces satisfying specific conditions.

Provides a structural framework for understanding symmetries in function spaces.

Abstract

The main result says that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be presented as a composition of a measurable transformation of a variable and multiplication by a function.