The HI extension of the standard HI spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910545690492928 |
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| author | Argyros, Spiros A. Manoussakis, Antonis Motakis, Pavlos |
| author_facet | Argyros, Spiros A. Manoussakis, Antonis Motakis, Pavlos |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_20030 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The HI extension of the standard HI spaces Argyros, Spiros A. Manoussakis, Antonis Motakis, Pavlos Functional Analysis 46B03, 46B06 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. |
| title | The HI extension of the standard HI spaces |
| topic | Functional Analysis 46B03, 46B06 |
| url | https://arxiv.org/abs/2407.20030 |