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Compactness in topological tensor products and operator spaces. (English) Zbl 0261.46022

MSC:
46B99 Normed linear spaces and Banach spaces; Banach lattices
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
47L50 Dual spaces of operator algebras
46M05 Tensor products in functional analysis
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References:
[1] Arlen Brown and Carl Pearcy, Spectra of tensor products of operators, Proc. Amer. Math. Soc. 17 (1966), 162 – 166. · Zbl 0141.32202
[2] Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. No. 16 (1955), 140 (French). · Zbl 0064.35501
[3] A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. São Paulo 8 (1953), 1 – 79 (French).
[4] J. R. Holub, Tensor product mappings, Math. Ann. 188 (1970), 1 – 12. · Zbl 0195.41601 · doi:10.1007/BF01435409 · doi.org
[5] Takashi Ichinose, On the spectra of tensor products of linear operators in Banach spaces., J. Reine Angew. Math. 244 (1970), 119 – 153. · Zbl 0198.47004 · doi:10.1515/crll.1970.244.119 · doi.org
[6] Robert Schatten, A Theory of Cross-Spaces, Annals of Mathematics Studies, no. 26, Princeton University Press, Princeton, N. J., 1950. · Zbl 0039.33503
[7] T. Terzioğlu, A characterization of compact linear mappings, Arch. Math. (Basel) 22 (1971), 76 – 78. · Zbl 0215.20902 · doi:10.1007/BF01222542 · doi.org
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