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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: https://doi.org/10.1090/memo/0806
MathSciNet review: 2053392
MSC: Primary 46B20; Secondary 46B03, 46B15, 46B26

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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