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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.4400 or http://arXiv.org/abs/0910.4400 or by email in unzipped form by transmitting an empty message with subject line uget 0910.4400 or in gzipped form by using subject line get 0910.4400 to: math@arXiv.org.
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alspach@fourier.math.okstate.edu