Banach-space characterization of Suslin-tree existence

Identify a natural Banach-space property \(\varphi\), not defined directly in terms of a combinatorial tree or graph, such that the existence of a Banach space with property \(\varphi\) is equivalent to the existence of a Suslin tree.

Background

The paper proves that the combinatorial Banach space generated by the finite chains of a Suslin tree has no uncountable equilateral set, but notes that the existence of a combinatorial Banach space of density $\omega_1$ without an uncountable equilateral set is not equivalent to the existence of a Suslin tree. The authors therefore seek an intrinsic Banach-space reformulation of the Suslin hypothesis, avoiding direct reference to trees or other combinatorial structures.