Strongly p-summing multilinear operators

By Verónica Dimant. 2003

93 citations recorded by the source corpus.

Abstract We define the concept of strongly p-summing multilinear operators and prove that they have properly defined Aron–Berner extensions. Some properties and examples are shown.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c21d159a4207c55ffd83d1808071a8e8e82d6fb4

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In Applied Mathematics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

On the Cohen strongly p-summing multilinear operators (2007, background): “[6] V. Dimant, Strongly p-summing multilinear mappings, J. Math.”
Comparing different classes of absolutely summing multilinear operators (2005, background): “This is the reason that has motivated in the last years the appearance of new definitions of multilinear p-summing operators: strongly p-summing operators [ 17 ], p-semi-integral operators [38], ... . Among these new classes, the class of multiple p-summing multilinear operators seems to be, up to n”
On composition ideals of multilinear mappings and homogeneous polynomials (2007, background): “Dimant [17] for real Banach spaces, but complex scalars work for our purposes as well.”
Ideals of polynomials generated by weakly compact operators (2006, unknown): “(c) From Alencar-Floret [4, Proposition 4.1] or Dimant-Zalduendo [44, Example 4.1] we have that P(n`p) is reflexive for p > n. QED 36 Remark.”
Multilinear extensions of Grothendieck’s theorem (2004, background): “Later on, motivated by the growth of the multilinear and polynomical theory of Banach spaces, different authors started the study of the p-summing multilinear operators between Banach spaces (see [1], [8], [14], [19], [21]).”