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Counterexample to a conjecture of Grothendieck. (English) Zbl 0506.46053


MSC:

46M05 Tensor products in functional analysis
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)

Citations:

Zbl 0064.355
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References:

[1] Apiola, H.: On the tensor product and product Hom(f, g) of compact operators in locally convex topological vector spaces. Ann. Acad. Sci. Fenn. Ser. A.544, 32 (1973) · Zbl 0259.46056
[2] Grothendieck, A.: Produits tensoriels topologiques et espaces nucléaires. Mem. Am. Math. Soc.16, 140 (1955) · Zbl 0123.30301
[3] Jarchow, H.: Locally convex spaces. Stuttgart: Teubner 1981 · Zbl 0466.46001
[4] John, K.: Zwei Charakterisierungen der nuklearen lokalkonvexen Räume. Comment. Math. Univ. Carolinae8, 117–128 (1967) · Zbl 0146.36501
[5] John, K., Zizler, V.: On a tensor product characterization of nuclearity. Math. Ann.244, 83–87 (1979) · Zbl 0417.46006
[6] John, K.: On tensor product characterization of nuclear spaces. Math. Ann.257, 341–353 (1981) · Zbl 0459.46005
[7] John, K., Junek, H.: A tensor product characterization of nuclear spaces. Wiss. Z. Pädag. Hochsch. ”Karl Liebknecht”. Potsdam25, 785–789 (1981) · Zbl 0514.46004
[8] John, K.: Tensor products and nuclearity. In: Proceedings on Banach space theory and its applications (Bucharest 1981); pp. 124–129. Lecture Notes in Mathematics, Vol. 991. Berlin, Heidelberg, New York: Springer 1983
[9] John, K., Bartík, V., Korbaš, J.: Tensor product of operators and the inequality of Horn (to appear)
[10] John, K.: Nuclearity and tensor products (to appear) · Zbl 0970.46511
[11] Köthe, G.: Topological vector spaces. II. Berlin, Heidelberg, New York: Springer 1979 · Zbl 0417.46001
[12] Pietsch, A.: Nuclear locally convex spaces. Berlin, Heidelberg, New York: Springer 1972 · Zbl 0308.47024
[13] Pietsch, A.: Operator ideals. Berlin: Deutscher Verlag der Wissenschaften 1978 · Zbl 0399.47039
[14] Pietsch, A.: Weyl numbers and eigenvalues of operators in Banach spaces. Math. Ann.247, 149–168 (1980) · Zbl 0428.47027
[15] Pisier, G.: Counterexamples to a conjecture of Grothendieck (preprint) · Zbl 0542.46038
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