Abstract
We derive a criterion for a Banach space to fail the uniform approximation property (UAP). This criterion is applied to prove thatc p spaces of matrices fail UAP ifp>80.
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References
S. Heinrich,Ultraproducts in Banach space theory, J. Reine Angew. Math.313 (1980), 72–104.
P. Jones,BMO and the Banach space approximation problem, Am. J. Math., to appear.
J. Lindenstrauss and L. Tzafriri,The uniform approximation property in Orlicz spaces, Isr. J. Math.23 (1976), 142–155.
A. Pelezynski and H. Rosenthal,Localization techniques in L p spaces, Studia Math.52 (1975), 263–289.
C. Samuel,Exemples d’espaces de Banach ayant la propriété de projection uniforme, Colloq. Math.43 (1980), 117–126.
A. Szankowski,B(H) does not have the approximation property, Acta Math.147 (1981), 89–108.
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Szankowski, A. On the uniform approximation property in Banach spaces. Israel J. Math. 49, 343–359 (1984). https://doi.org/10.1007/BF02760959
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DOI: https://doi.org/10.1007/BF02760959