Geodesic
Three-space problems for the approximation property
Journal of the European Mathematical Society, Tome 11 (2009) no. 2, pp. 273-282 Cet article a éte moissonné depuis la source EMS Press

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It is shown that there is a subspace Zq​ of lq​ for 12 which is isomorphic to lq​ such that lq​/Zq​ does not have the approximation property. On the other hand, for 2∞ there is a subspace Yp​ of lp​ such that Yp​ does not have the approximation property (AP) but the quotient space lp​/Yp​ is isomorphic to lp​ . The result is obtained by defining random "Enflo-Davie spaces" Yp​ which with full probability fail AP for all 2≤∞ and have AP for all 1≤p≤2. For 1≤ 2, Yp​ are isomorphic to lp​.
DOI : 10.4171/jems/150
Classification : 46-XX, 00-XX
Keywords: Quotients of Banach spaces, approximation property 
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     author = {A. Szankowski},
     title = {Three-space problems for the approximation property},
     journal = {Journal of the European Mathematical Society},
     pages = {273--282},
     year = {2009},
     volume = {11},
     number = {2},
     doi = {10.4171/jems/150},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/150/}
}
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A. Szankowski. Three-space problems for the approximation property. Journal of the European Mathematical Society, Tome 11 (2009) no. 2, pp. 273-282. doi: 10.4171/jems/150

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