The cofinal property of the Reflexive Indecomposable Banach spaces

TL;DR

This paper demonstrates that every separable reflexive Banach space can be embedded into or represented as a quotient of special reflexive spaces with indecomposability or saturation properties, revealing new structural insights.

Contribution

It proves that all separable reflexive Banach spaces are quotients or subspaces of reflexive Hereditarily Indecomposable and saturated spaces, advancing the understanding of their structural properties.

Findings

Every separable reflexive Banach space is a quotient of a reflexive Hereditarily Indecomposable space.

Every such space is isomorphic to a subspace of a reflexive Indecomposable space.

They are also quotients of reflexive $ ext{ell}_p$ saturated and $c_0$ saturated spaces.

Abstract

It is shown that every separable reflexive Banach space is a quotient of a reflexive Hereditarily Indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive Indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $\ell_p$ saturated space with $1<p<\infty$ and of a $c_0$ saturated space.