Universal disposition is not a 3-space property

TL;DR

This paper demonstrates that the properties of (almost) universal disposition and separable universal disposition in Banach spaces do not hold as 3-space properties, challenging previous assumptions about their structural stability.

Contribution

It provides the first proof that these universal disposition properties are not preserved under 3-space extensions in Banach space theory.

Findings

Universal disposition is not a 3-space property.

Separable universal disposition is not a 3-space property.

Challenges assumptions about stability of these properties.

Abstract

We prove that (almost) universal disposition and separable universal disposition of Banach spaces are not $3$-space properties.