Multilinear extensions of Grothendieck’s theorem

By F. Bombal, David Pérez-García, Ignacio Villanueva. 2004

133 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/89b2d408a42bf477bd4906d2919a48915bd3b745

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Citations in the corpus

Summation of coefficients of polynomials on $\ell_{p}$ spaces (2013, background): “[18, 7]) if there is K > 0 such that for every (x (j) ij ) Nj ij=1 ⊆ Xj , for j = 1, .”
Complex interpolation and summability properties of multilinear operators (2010, methodology): “We will need the following lemma due to David Perez-Garcia [24, Teorema 5.2] and Marcela Souza [30, Teorema 1.7.3] (see also [ 6, Theorem 3.2 ]):”
Multiple summing operators on Banach spaces (2003, methodology): “Remark 3.5. This result improves the results given in [ 3, Section 5 ]. It must be noticed that this theorem is essentially contained in the work of H.P.”
Multiple summing maps: Coordinatewise summability, inclusion theorems and p-Sidon sets (2017, methodology): “Following [8] and [17], for r ≥ 1 and p = (p1, .”
Comparing different classes of absolutely summing multilinear operators (2005, background): “1 p 6 ] and 6 appears with three different proofs in [6], [39] and [40].”
On the Cohen strongly p-summing multilinear operators (2007, background): “There are many definitions generalizing the notion of summability to multilinear operators; the definitions of absolutely p-summing, r-dominated and strongly p-summing multilinear operators (there are also other definitions such as the class of the multiple p-summing multilinear operators, see [3,12”
A new multilinear insight on Littlewood's 4/3-inequality (2009, unknown): “For related results see [1,6,8,10,34,36,42].”
Unbounded Violation of Tripartite Bell Inequalities (2007, background): “Since Grothendieck stated his Theorem, a lot of effort has been devoted to find suitable multilinear generalizations (see for instance [11, 12, 17, 51, 54, 65]).”
Bohr’s strip for vector valued Dirichlet series (2008, background): “the associated symmetric m-linear mapping on � ∞. Then we know from [ 2, Theorem 3.2 ] that”