[Banach] Abstract of a paper by Kevin Beanland and Frank Sanacory

This is an announcement for the paper "Spreading models in the duals of Schlumprecht-type spaces" by Kevin Beanland and Frank Sanacory.

Abstract: We show that the dual of Schlumprecht's space $S^*$ and the dual of Gowers and Maurey's HI space each contain a $c_0$ spreading model and that for each $1 < p < \infty$ and $1/p+1/q=1$, the dual of the $p$-convexification of Schlumprecht's space and the dual of its HI counterpart, constructed by Neil Dew, each contain an $\ell_q$ spreading model. The existence of a $c_0$ spreading model in $S^*$ solves a problem of S. A. Argyros. We also give a general criteria for the existence of a bounded non-compact operator and use this to show that there exist strictly singular non-compact operators on each of these spaces.

Archive classification: math.FA

Mathematics Subject Classification: 46B28

Remarks: 14 pages

The source file(s), CoinSstarfinal.bbl: 3840 bytes

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http://front.math.ucdavis.edu/0910.4400

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http://arXiv.org/abs/0910.4400

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