Methods in the Theory of Hereditarily Indecomposable Banach Spaces
Argyros, Spiros A., Tolias, Andreas
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^*
Kategori:
Tahun:
2004
Penerbit:
American Mathematical Society
Bahasa:
english
Halaman:
114
ISBN 10:
1470404079
ISBN 13:
9781470404079
Nama seri:
Memoires of American Mathematical Society 806
File:
DJVU, 946 KB
IPFS:
,
english, 2004