A solution to Banach conjecture

TL;DR

This paper proves Banach's isometric subspace problem in finite-dimensional spaces by constructing global linear maps from local properties, extending previous results by Gromov.

Contribution

It provides a complete proof of Banach's conjecture in finite dimensions, building on and extending Gromov's earlier work.

Findings

Established the full proof of Banach's isometric subspace problem

Constructed global linear maps from local continuity properties

Extended Gromov's results to a complete solution

Abstract

In this paper, we begin by constructing global linear maps on (n-2)-dimensional subspaces, derived from the local continuity of linear transformations among central sections of a convex body. Using these linear maps, we subsequently establish a full proof of Banach's isometric subspace problem in finite-dimensional spaces, extending Gromov's earlier results.