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On multilinear mappings of nuclear type. (English) Zbl 0807.46022

Summary: The space of multilinear mappings of nuclear type \((s; r_ 1,\dots, r_ n)\) between Banach spaces is considered, some of its properties are described (including the relationship with tensor products) and its topological dual is characterized as a Banach space of absolutely summing mappings.

MSC:

46B28 Spaces of operators; tensor products; approximation properties
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
46E40 Spaces of vector- and operator-valued functions
46G20 Infinite-dimensional holomorphy
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