Isometric uniqueness of a complementably universal Banach space for Schauder decompositions

TL;DR

This paper introduces an isometric version of a universal Banach space with Schauder decompositions, unifying several known universal spaces through isometric properties.

Contribution

It constructs an isometric complementably universal Banach space with Schauder decompositions, linking Pe{ }czy{\'n}ski's and Kadec's universal spaces.

Findings

The space is isometric to Pe{ }czy{\'n}ski's universal basis space.

It is also isomorphic to Kadec's complementably universal space.

The space possesses the bounded approximation property.

Abstract

We present an isometric version of the complementably universal Banach space $\mathbb{P}$ with a Schauder decomposition. The space $\mathbb{P}$ is isomorphic to Pe{\l}czy\'nski's space with a universal basis as well as to Kadec' complementably universal space with the bounded approximation property.