Geodesic
Banach spaces of bounded Szlenk index II
D. Freeman 1   ; E. Odell 2   ; Th. Schlumprecht 1   ; A. Zsák 3
1 Department of Mathematics Texas A&M University College Station, TX 77843, U.S.A.
2 Department of Mathematics The University of Texas 1 University Station C1200 Austin, TX 78712, U.S.A.
3 School of Mathematics University of Leeds Leeds, LS2 9JT, United Kingdom
Fundamenta Mathematicae, Tome 205 (2009) no. 2, pp. 161-177 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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For every $\alpha \omega _1$ we establish the existence of a separable Banach space whose Szlenk index is $\omega ^{\alpha \omega +1}$ and which is universal for all separable Banach spaces whose Szlenk index does not exceed $\omega ^{\alpha \omega }$. In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with Tsirelson type upper estimates.
DOI : 10.4064/fm205-2-5
Keywords: every alpha omega establish existence separable banach space whose szlenk index omega alpha omega which universal separable banach spaces whose szlenk index does exceed omega alpha omega order prove result provide intrinsic characterization which banach spaces embed space admitting fdd tsirelson type upper estimates

D. Freeman  1   ; E. Odell  2   ; Th. Schlumprecht  1   ; A. Zsák  3

1 Department of Mathematics Texas A&M University College Station, TX 77843, U.S.A.
2 Department of Mathematics The University of Texas 1 University Station C1200 Austin, TX 78712, U.S.A.
3 School of Mathematics University of Leeds Leeds, LS2 9JT, United Kingdom 
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D. Freeman; E. Odell; Th. Schlumprecht; A. Zsák. Banach spaces of bounded Szlenk index II. Fundamenta Mathematicae, Tome 205 (2009) no. 2, pp. 161-177. doi: 10.4064/fm205-2-5

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