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Reverse inclusions for multiple summing operators. (English) Zbl 1154.47014
In [D. Pérez–García, Stud. Math. 165, No. 3, 275–290 (2004; Zbl 1064.47057)], some inclusion theorems were proven for the class of multilinear absolutely summing operators. In the paper under review, the author utilize some ideas from [J. Diestel, H. Jarchow and A. Tonge, “Absolutely summing operators” (Cambridge Studies in Advanced Mathematics 43; Cambridge Univ. Pr.) (1995; Zbl 0855.47016)] to prove some reverse inclusion theorems, as well as some coincidence results which mainly concentrate on the class of \((q, 2)\)-summing operators.

MSC:
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
46G25 (Spaces of) multilinear mappings, polynomials
47H60 Multilinear and polynomial operators
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