Game-theoretic characterization of the Gurarii space

TL;DR

This paper introduces an infinite game approach to characterize the Gurarii space, demonstrating that one player can ensure the union's completion is isometric to it, regardless of the opponent's moves.

Contribution

It provides a novel game-theoretic framework for understanding the Gurarii space, connecting infinite games with Banach space theory.

Findings

Existence of a winning strategy for one player in the game

The union of the chain is linearly isometric to the Gurarii space

The approach offers new insights into the structure of the Gurarii space

Abstract

We present a simple and natural infinite game building an increasing chain of finite-dimensional Banach spaces. We show that one of the players has a strategy with the property that, no matter how the other player plays, the completion of the union of the chain is linearly isometric to the Gurarii space.