Methods in the theory of hereditarily indecomposable Banach spaces / Spiros A. Argyros, Andreas Tolias.
Introduction General results about H.I. spaces Schreier families and repeated averages The space ${X= T [G, (\mathcal{S}_{n_j}, {\tfrac {1}{m_j})}_{j}, D]}$ and the auxiliary space ${T_{ad}}$ The basic inequality Special convex combinations in $X$ Rapidly increasing sequences Defining $D$ to obtain...
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| Language: | English |
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Providence, R.I. :
American Mathematical Society,
©2004.
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| Series: | Memoirs of the American Mathematical Society ;
no. 806. |
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Table of Contents:
- 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 $X̂*_G$ 11. Complemented embedding of $l̂p$, $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.