# Isometries of combinatorial Banach spaces

## TL;DR

This paper characterizes all isometries of combinatorial Banach spaces, showing they are essentially permutations and sign changes of the basis, with specific results for Schreier spaces.

## Contribution

It provides a complete description of isometries in combinatorial Banach spaces, including Schreier spaces, extending understanding of their symmetry properties.

## Key findings

- Isometries are permutations and sign changes of the basis.
- In Schreier spaces, isometries are only sign changes.
- Results apply to both real and complex spaces.

## Abstract

We prove that every isometry between two combinatorial spaces is determined by a permutation of the canonical unit basis combined with a change of signs. As a consequence, we show that in the case of Schreier spaces, all the isometries are given by a change of signs of the elements of the basis. Our results hold for both the real and the complex cases.