METHODS IN THE THEORY OF HEREDITARILY INDECOMPOSABLE BANACH SPACES by Spiros A. Argyros, Andreas Tolias ( 9780821835210 )

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Title:

METHODS IN THE THEORY OF HEREDITARILY INDECOMPOSABLE BANACH SPACES

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Format:

Paperback

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ISBN 10:

0821835211

ISBN 13:

9780821835210

Publisher:

AMERICAN MATHEMATICAL SOCIETY

Pub. date:

1 January, 2004

Series:

Memoirs of the American Mathematical Society No. 170

Pages:

114

Description:

A general method producing Hereditarily Indecomposable (H I) Banach spaces is provided. We apply this method to construct a nonseparable H I Banach space $Y$. This space is the dual, as well as the second dual, of a separable H I Banach space.

Synopsis:

A general method producing Hereditarily Indecomposable (H.I.) Banach spaces is provided. We apply this method to construct a nonseparable H.I. Banach space $Y$. This space is the dual, as well as the second dual, of a separable H.I. Banach space. Moreover the space of bounded linear operators ${\mathcal{L}}Y$ consists of elements of the form $\lambda I+W$ where $W$ is a weakly compact operator and hence it has separable range. Another consequence of the exhibited method is the proof of the complete dichotomy for quotients of H.I. Banach spaces. Namely we show that every separable Banach space $Z$ not containing an isomorphic copy of $\ell^1$ is a quotient of a separable H.I. space $X$. Furthermore the isomorph of $Z^*$ into $X^*$, defined by the conjugate operator of the quotient map, is a complemented subspace of $X^*$.

Publication:

Imprint:

American Mathematical Society

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Returnable

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