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arXiv · 2407.20030

The HI extension of the standard HI spaces

Spiros A. Argyros·Antonis Manoussakis·Pavlos Motakis
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Abstract

A Hereditarily Indecomposable (HI) Banach space $X$ admits an HI extension if there exists an HI space $Z$ such that $X$ is isomorphic to a subspace $Y$ of $Z$ and $Z/Y$ is of infinite dimension. The problem whether or not every HI space admits an HI extension is attributed to A. Pelczynski. In this paper we present a method to define HI-extensions of the standard HI spaces, a class which includes the Gowers-Maurey space, asymptotic $\ell_{p}$-HI spaces and others.

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Spiros A. Argyros, Antonis Manoussakis, Pavlos Motakis. 2024-07-29. The HI extension of the standard HI spaces. https://arxiv.org/abs/2407.20030

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