# Methods in the theory of hereditarily indecomposable Banach spaces

### About this Title

**Spiros A. Argyros** and **Andreas Tolias**

Publication: Memoirs of the American Mathematical Society

Publication Year
2004: Volume 170, Number 806

ISBNs: 978-0-8218-3521-0 (print); 978-1-4704-0407-9 (online)

DOI: http://dx.doi.org/10.1090/memo/0806

MathSciNet review: 2053392

MSC: Primary 46B20; Secondary 46B03, 46B15, 46B26

### Table of Contents

**Chapters**

- Introduction
- 1. General results about H.I. spaces
- 2. Schreier families and repeated averages
- 3. The space $X = T[G, (\mathcal {S}_{n_j}, 1/m_j)_j, D]$ and the auxiliary space $T_{ad}$
- 4. The basic inequality
- 5. Special convex combinations in $X$
- 6. Rapidly increasing sequences
- 7. Defining $D$ to obtain a H.I. space $X_G$
- 8. The predual $(X_G)_*$ of $X_G$ is also H.I.
- 9. The structure of the space of operators $\mathcal {L}(X_G)$
- 10. Defining $G$ to obtain a nonseparable H.I. space $X^*_G$
- 11. Complemented embedding of $l^p$, $1 \leq p < \infty $, in the duals of H.I. spaces
- 12. Compact families in $\mathbb {N}$
- 13. The space $X_G = T[G, (\mathcal {S}_\xi , 1/m_j)_j, D]$ for an $\mathcal {S}_\xi $ bounded set $G$
- 14. Quotients of H.I. spaces