Interpolating hereditarily indecomposable Banach spaces

TL;DR

This paper demonstrates that every Banach space either contains an  or has an infinite-dimensional subspace that is a quotient of a hereditarily indecomposable (H.I.) Banach space, including all L^p spaces for 1<p<.

Contribution

It introduces a method to interpolate hereditarily indecomposable Banach spaces, showing broad classes of spaces are quotients of H.I. spaces, expanding understanding of Banach space structure.

Findings

Every Banach space contains  or has an H.I. quotient subspace.

L^p(), 1<p<, is a quotient of an H.I. Banach space.

Provides a new perspective on the structure of Banach spaces through interpolation.

Abstract

It is shown that every Banach space either contains $\ell ^1$ or it has an infinite dimensional closed subspace which is a quotient of a H.I. Banach space.Further on, $L^p(\lambda )$, $1<p<\infty $, is a quotient of a H.I Banach space.