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References
Davis, W., Johnson, W.B.: Compact, non-nuclear operators. Stud. Math.51, 81–85 (1974)
Diestel, J.: Sequences and series in Banach spaces. (Graduate texts in math. vol. 92) Berlin Heidelberg New York: Springer 1984
Grothendieck, A.: Produits tensoriels topologiques espaces nucléaires. Mem. Am. Math. Soc.16 (1955)
Grothendieck, A.: Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat. São Paulo8, 1–79 (1956)
Jarchow, H.: On Hilbert-Schmidt spaces. Rend. Circ. Mat. Palermo (Suppl)II (2), 153–160 (1982)
Jarchow, H.: Locally convex spaces. Stuttgart: Teubner 1981
John, K.: Tensor products and nuclearity. Lect. Notes Math., Vol. 991, pp. 124–129 Berlin Heidelberg New York: Springer 1983
John, K.: Counterexample to a conjecture of Grothendieck. Math. Ann.265, 169–179 (1983)
John, K.: Tensor products of several spaces and nuclearity. Math. Ann.269, 333–356 (1984)
John, K.: Nuclearity and tensor products. Doĝa Tr. J. Math.10, 125–135 (1986)
John, K.: Some remarks on the compact non-nuclear operator problem. Lond. Math. Soc. Lect. Note Ser.150, 140–144 (1989)
John, K., Zizler, V.: Projections in dual weakly compactly generated Banach spaces. Stud. Math.49, 41–50 (1973)
Johnson, W.B.: On finite dimensional subspaces of Banach spaces with local unconditional structure. Stud. Math.51, 225–240 (1974)
Johnson, W.B., König, H., Maurey, B., Retherford, R.: Eigenvalues ofp-summing andl p -type operators in Banach spaces. J. Funct. Anal.32, 353–380 (1979)
Kalton, N.J.: Spaces of compact operators. Math. Ann.208, 267–278 (1974)
Lindenstrauss, J.: On non-separable reflexive Banach spaces. Bull. Am. Math. Soc.72, 967–970 (1966)
Lindenstrauss, J., Pelczyński, A.: Absolutely summing operators in ℒ p -spaces and their application. Stud. Math.29, 275–326 (1968)
Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces. I. Berlin Heidelberg New York: Springer 1977
Niculescu, C.P.: New progress on ℒ(E,F)=N 1(E,F). An. Univ. Craiova, Ser. Mat. Fiz.-Chim.6, 27–29 (1978)
Pietsch, A.: Nuclear locally convex spaces. Berlin Heidelberg New York: Springer 1972
Pietsch, A.: Operator ideals. Berlin: Deutscher Verlag der Wissenschaften 1978
Pisier, G.: Un théorème sur les opérateurs linéaires entre espaces de Banach qui se factorisent par un espace de Hilbert. Ann. Sci. Ec. Norm. Supér., IV. Sér.13, 23–43 (1980)
Pisier, G.: Counterexamples to a conjecture of Grothendieck. Acta. Math.151, 180–208 (1983)
Pisier, G.: Factorization of linear operators and geometry of Banach spaces. CBMS Regional conference, series n0 60, AMS, 1-154 (1986)
Singer, I.: Bases in Banach spaces. II. Berlin Heidelberg New York: Springer 1981
Stegall, C.P., Retherford, J.R.: Fully nuclear and completely nuclear operators with applications to ℒ1 and ℒ∞-spaces. Trans. Am. Math. Soc.163, 457–492 (1972)
Tseitlin, I.I.: On a particular case of the existence of a compact operator which is not nuclear. Funkts. Anal. Prilozh6, 102 (1979)
Tseitlin, I.I.: The extreme points of the unit ball of certain spaces of operators. Mat. Zametki20, 521–527 (1976)
Ruess, W., Stegall, Ch.: Extreme points in duals of operator spaces. Math. Ann.261, 535–546 (1982)
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To the memory of Zdeněk Frolik
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John, K. On the compact non-nuclear operator problem. Math. Ann. 287, 509–514 (1990). https://doi.org/10.1007/BF01446908
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DOI: https://doi.org/10.1007/BF01446908