A remark on spaces of affine continuous functions on a simplex

TL;DR

This paper provides a counterexample in the theory of affine continuous functions on a Choquet simplex, showing that certain infinite-dimensional spaces do not contain a subspace isometric to c, challenging previous assumptions.

Contribution

It constructs a specific example of an infinite-dimensional affine function space that lacks a subspace isometric to c, disproving a prior result in Banach space theory.

Findings

Counterexample of an affine function space without a c-isometric subspace

Disproof of a previously claimed result in Banach space subspace structure

Insight into the geometry of affine function spaces on simplices

Abstract

We present an example of an infinite dimensional separable space of affine continuous functions on a Choquet simplex that does not contain a subspace linearly isometric to $c$. This example disproves a result stated in M. Zippin. On some subspaces of Banach spaces whose duals are $L_1$ spaces. Proc. Amer. Math. Soc. 23, (1969), 378-385.