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Characterization of the maximal ideal of operators associated to the tensor norm defined by an Orlicz function. (English) Zbl 0993.46045
Operator ideals of \(p\)-nuclear and \(p\)-integral operators were defined by A. Persson and A. Pietsch [Studia Math. 33, 19-62 (1969; Zbl 0189.43602)], who used for their definitions the classical spaces \(\ell_p\). Operator ideals of \(H^c\)-nuclear and \(H^c\)-integral operators are defined in the article under review. Their definitions use an Orlicz sequence space \(\ell_H\), where the Orlicz function \(H(t)\) satisfies the \(\Delta_2\)-condition, and also a certain convexification procedure (denoted by superscript \(c\)) is used. Properties of the \(H^c\)-nuclear and \(H^c\)-integral operators are studied and a characterization of \(H^c\)-integral operators is given by a factorization theorem.

46M05 Tensor products in functional analysis
47L20 Operator ideals
46A45 Sequence spaces (including Köthe sequence spaces)
46A32 Spaces of linear operators; topological tensor products; approximation properties
Full Text: DOI
[1] Defant, A. and K. Floret: Tensor Norms and Operator Ideals (North Holland Math. Studies). Amsterdam: North Holland Publ. Comp. 1993. · Zbl 0774.46018
[2] Haydom, R., Levy, M. and Y. Raynaud: Randomly Normed Spaces. Paris: Hermann 1991. · Zbl 0771.46023
[3] Heinrich, S.: Ultraproducts in Banach spaces theory. J. Reine Angew. Math. 313 (1980), 72 - 104. · Zbl 0412.46017 · doi:10.1515/crll.1980.313.72 · eudml:152195
[4] Hollstein, R.: Inductive limits and \epsilon -tensor products. J. Reine Angew. Math. 319 (1980), 38 - 62. · Zbl 0426.46053 · doi:10.1515/crll.1980.319.38 · crelle:GDZPPN002197693 · eudml:152277
[5] Lindenstrauss, J. and L. Tzafriri: Classical Banach Spaces, Vol. II. Berlin et al.: Springer- Verlag 1979. · Zbl 0403.46022
[6] Loaiza, G., López Molina, J. A. and M. J. Rivera: Normas tensoriales y espacios de oper- adores factorables a través de espacios de Orlicz.. Revista Mat. de la Univ. Tecnológica de Pereira (to appear).
[7] Loaiza, G., López Molina, J. A. and M. J. Rivera: On absolutely summing, nuclear and integral operators associated to an Orlicz function. Preprint.
[8] Meyer-Nieberg, P. Banach Lattices. Berlin et al.: Springer-Verlag 1991. · Zbl 0743.46015
[9] Schaefer, H. H.: Banach Lattices and Positive Operators. Berlin et al.: Springer-Verlag 1974.
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