Abstract of a paper by Spiros A. Argyros and Pavlos Motakis
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 or http://arXiv.org/abs/1206.1279
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