The universal Banach space with a $K$-suppression unconditional basis

TL;DR

This paper constructs a universal Banach space with a normalized $K$-suppression unconditional Schauder basis for any constant $K \,\geq\ 1$, using Fra"issé theory.

Contribution

It introduces a novel construction of a universal Banach space with a $K$-suppression unconditional basis via Fra"issé theory, expanding the understanding of Banach space universality.

Findings

Existence of a universal Banach space with $K$-suppression unconditional basis for all $K \,\geq\ 1$

Application of Fra"issé theory to Banach space construction

Framework for further exploration of universal structures in functional analysis

Abstract

Using the technique of Fra\"iss\'e theory, for every constant $K\ge 1$ we consruct a universal object in the class of Banach spaces with normalized $K$-suppression unconditional Schauder bases.