arXiv subjects

Samuel García-Hernández

Publications and source records attributed to Samuel García-Hernández.

3 recordsLinked to original sources

arXiv2018

The Duality between Ideals of Multilinear Operators and Tensor Norms

We develop the duality theory between ideals of multilinear operators and tensor norms that arises from the geometric approach of $Σ$-operators. To this end, we introduce and develop the notions of $Σ$-ideals of multilinear operators and $Σ$-tensor norms. We establish the foundations of this theory by proving a representation theorem for maximal $Σ$-ideals of multilinear operators by finitely generated $Σ$-tensor norms and a duality theorem for $Σ$-tensor norms. For these notions we also develop basic theory and present concrete examples.

math.FA↗

arXiv2018

$(p,q)$-Dominated Multilinear Operators and Lapresté tensor norms

We introduce a notion of $(p,q)$-dominated multilinear operators which stems from the geometrical approach provided by $Σ$-operators. We prove that $(p,q)$-dominated multilinear operators can be characterized in terms of their behavior on finite sequences and in terms of their relation with a Lapresté tensor norm. We also prove that they verify a generalization of the Pietsch's Domination Theorem and Kwapień's Factorization Theorem. Also, we study the collection $\mathcal{D}_{p,q}$ of all $(p,q)$-dominated multilinear operators showing that $\mathcal{D}_{p,q}$ has a maximal ideal demeanor and that the Lapresté norm has a finitely generated behavior.

math.FA↗

arXiv2018

Multilinear Operators Factoring through Hilbert Spaces

We characterize those bounded multilinear operators that factor through a Hilbert space in terms of its behavior in finite sequences. This extends a result, essentially due to S. Kwapień, from the linear to the multilinear setting. We prove that Hilbert-Schmidt and Lipschitz $2$-summing multilinear operators naturally factor through a Hilbert space. It is also proved that the class $Γ$ of all multilinear operators that factor through a Hilbert space is a maximal multi-ideal; moreover, we give an explicit formulation of a finitely generated tensor norm $γ$ which is in duality with $Γ$.

math.FA↗