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Duality between spaces of \(p\)-summable sequences, \((p,q)\)-summing operators and characterizations of nuclearity. (English) Zbl 0304.47025


MSC:

47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
46A45 Sequence spaces (including Köthe sequence spaces)
46M05 Tensor products in functional analysis
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References:

[1] Cohen, J. S.: Absolutelyp-summing,p-nuclear operators, and their conjugates. Math. Ann.201, 177-200 (1973) · Zbl 0233.47019 · doi:10.1007/BF01427941
[2] Dean, D. W.: The equationL(E, X**)=L(E, X)** and the principle of local reflexivity. Proc. Amer. Math. Soc.40, 146-148 (1973)
[3] Grothendieck, A.: Produits tensoriels topologiques et espaces nucléaires. Mem. Amer. Math. Soc.16, (1955) · Zbl 0123.30301
[4] Grothendieck, A.: Sur certaines classes de suites dans les espaces de Banach et le théorème de Dvoretzky-Rogers. Bol. Soc. Mat. São Paulo8, 81-110 (1956)
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[7] Pietsch, A.: Nuclear locally convex spaces. Berlin-Heidelberg-New York: Springer 1972 · Zbl 0308.47024
[8] Pietsch, A.: Absolutp-summierende Abbildungen in normierten Räumen. Studia Math.28, 333-353 (1967) · Zbl 0156.37903
[9] Pietsch, A.: Adjungierte normierte Operatorenideale. Math. Nachr.48, 189-211 (1971) · Zbl 0233.46084 · doi:10.1002/mana.19710480114
[10] Pietsch, A.: Theorie der Operatorenideale (Zusammenfassung). Friedrich-Schiller-Universität, Jena 1972 · Zbl 0238.46067
[11] Schaefer, H. H.: Topological vector spaces, third printing. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0212.14001
[12] Schwarz, H. U.: Adjungierte Operatorenideale. Math. Nachr.55, 293-308 (1973) · Zbl 0258.47034 · doi:10.1002/mana.19730550117
[13] Simons, S.: Local reflexivity and (p, q)-summing maps. Math. Ann.198, 335-344 (1972) · Zbl 0231.46033 · doi:10.1007/BF01419563
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