The space of all bounded operators on Hilbert space does not have the approximation property
Séminaire d'Analyse fonctionnelle (dit "Maurey-Schwartz") (1978-1979), Talk no. 14 et 15, 21 p.
@article{SAF_1978-1979____A13_0,
     author = {Szankowski, A.},
     title = {The space of all bounded operators on {Hilbert} space does not have the approximation property},
     journal = {S\'eminaire d'Analyse fonctionnelle (dit "Maurey-Schwartz")},
     note = {talk:14 et 15},
     pages = {1-21,A1-A7},
     publisher = {Ecole Polytechnique, Centre de Math\'ematiques},
     year = {1978-1979},
     mrnumber = {557369},
     zbl = {0413.46003},
     language = {en},
     url = {http://www.numdam.org/item/SAF_1978-1979____A13_0/}
}
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Szankowski, A. The space of all bounded operators on Hilbert space does not have the approximation property. Séminaire d'Analyse fonctionnelle (dit "Maurey-Schwartz") (1978-1979), Talk no. 14 et 15, 21 p. http://www.numdam.org/item/SAF_1978-1979____A13_0/

[1] P. Enflo, A counterexample to the approximation property in Banach spaces, Acta Math. 130 (1973), p. 309-317. | MR | Zbl

[2] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Memoir AMS 16 (1955). | MR | Zbl