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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.

MSC:
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
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