ENGLISH

Methods in the Theory of Hereditarily Indecomposable Banach Spaces

By Andreas , Argyros , Spiros A.; Tolias

Book information

Publisher
American Mathematical Society
Year
2004
ISBN
0-8218-3521-1, 9780821835210, 9781470404079, 1470404079
Language
english
Format
DJVU
Filesize
946 kB (969055 bytes)
Series
Memoires of American Mathematical Society 806
Pages
114\124
Library
kolxoz
Time added
2017-10-15 16:00:00
Normed linear spaces;Banach spaces;NORMIERTE RÄUM

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. 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^*

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