Szankowski, Andrzej B(H) does not have the approximation property. (English) Zbl 0486.46012 Acta Math. 147, 89-108 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 36 Documents MSC: 46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces 46B20 Geometry and structure of normed linear spaces 46A32 Spaces of linear operators; topological tensor products; approximation properties 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 46M05 Tensor products in functional analysis 47L05 Linear spaces of operators 47L30 Abstract operator algebras on Hilbert spaces 46L05 General theory of \(C^*\)-algebras 46L10 General theory of von Neumann algebras 05A17 Combinatorial aspects of partitions of integers 15B57 Hermitian, skew-Hermitian, and related matrices Keywords:approximation property; Enflo’s criterion; space of bounded linear operators on a Hilbert space; separable C*-algebras; regular partitions; strictly equivalent matrices; Hadamard matrices; gliding hump Citations:Zbl 0064.355; Zbl 0413.46003 PDFBibTeX XMLCite \textit{A. Szankowski}, Acta Math. 147, 89--108 (1981; Zbl 0486.46012) Full Text: DOI References: [1] Choi, M. &Effros, E., NuclearC *-algebras and the approximation property.Amer. J. Math., 100 (1978), 61–79. · Zbl 0397.46054 · doi:10.2307/2373876 [2] Enflo, P., A counterexample to the approximation property in Banach spaces.Acta Math., 130 (1973), 309–317. · Zbl 0267.46012 · doi:10.1007/BF02392270 [3] Grothendieck, A., Produits tensoriels topologiques et espaces nuclearies.Memoirs Amer. Math. Soc., 16 (1955). · Zbl 0123.30301 [4] Haagerup, U., An example of a non-nuclearC *-algebra, which has the metric approximation property.Invent. Math., 50 (1979), 279–293. · Zbl 0408.46046 · doi:10.1007/BF01410082 [5] Lance, C., On nuclearC *-algebras,J. Functional Analysis, 12 (1973), 157–176. · Zbl 0252.46065 · doi:10.1016/0022-1236(73)90021-9 [6] Lindenstrauss, J. & Tzafriri, L.,Classical Banach Spaces, Vol. 1. Springer-Verlag 1977. · Zbl 0362.46013 [7] Szankowski, A., The space of all bounded operators on Hilbert space does not have the approximation property, exposé, XIV–XV.Seminaire d’analyse fonctionnelle, 1978–79, Ecole Polytechnique. [8] Takesaki, M., On the cross-norm of the direct product ofC *-algebras.Tohoku Math. J., 16 (1964), 111–122. · Zbl 0127.07302 · doi:10.2748/tmj/1178243737 [9] Wasserman, S., On tensor products of certain groupC *-algebras.J. Functional Analysis, 23 (1976), 239–254. · Zbl 0358.46040 · doi:10.1016/0022-1236(76)90050-1 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.