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Strongly \(p\)-summing multilinear operators. (English) Zbl 1043.47018

The author defines a concept of strongly \(p\)-summing multilinear operator in order to lift properties of absolutely \(p\)-summing linear operators to the multilinear and polynomial case. It is shown that the space of strongly \(p\)-summing multilinear operators is a Banach space, there is a sort of Pietsch domination theorem, and an Aron-Berner extension.

MSC:

47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47H60 Multilinear and polynomial operators
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References:

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