Saturated extensions, the attractors method and Hereditarily James Tree Space

TL;DR

This paper constructs examples of hereditarily indecomposable Banach spaces with no reflexive subspaces, analyzing their duals and operator spaces using saturated extensions and attractors.

Contribution

It introduces new constructions of HI Banach spaces without reflexive subspaces using saturated extensions and the attractors method, expanding understanding of their structure.

Findings

Examples of HI Banach spaces with no reflexive subspaces

Detailed analysis of dual spaces and operator spaces

Application of saturated extensions and attractors in space construction

Abstract

In the present work we provide a variety of examples of HI Banach spaces containing no reflexive subspace and we study the structure of their duals as well as the spaces of their linear bounded operators. Our approach is based on saturated extensions of ground sets and the method of attractors.