This is an announcement for the paper "A hereditarily indecomposable Banach space with rich spreading model structure" by Spiros A. Argyros and Pavlos Motakis.
Abstract: We present a reflexive Banach space $\mathfrak{X}_{_{^\text{usm}}}$ which is Hereditarily Indecomposable and satisfies the following properties. In every subspace $Y$ of $\mathfrak{X}_{_{^\text{usm}}}$ there exists a weakly null normalized sequence ${y_n}_n$, such that every subsymmetric sequence ${z_n}_n$ is isomorphically generated as a spreading model of a subsequence of ${y_n}_n$. Also, in every block subspace $Y$ of $\mathfrak{X}_{_{^\text{usm}}}$ there exists a seminormalized block sequence ${z_n}$ and $T:\mathfrak{X}_{_{^\text{usm}}}\rightarrow\mathfrak{X}_{_{^\text{usm}}}$ an isomorphism such that for every $n\in\mathbb{N}$ $T(z_{2n-1}) = z_{2n}$. Thus the space is an example of an HI space which is not tight by range in a strong sense.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B06, 46B25, 46B45
Remarks: 36 pages, no figures
Submitted from: pmotakis@central.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.1279
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