Infinite dimensional extension of A. P. Calderòn's theorem on positive semidefinite biquadratic forms.
Integral polynomials on Banach spaces not containing
We give new characterizations of Banach spaces not containing in terms of integral and -dominated polynomials, extending to the polynomial setting a result of Cardassi and more recent results of Rosenthal.
L-sets and the Pelczynski-Pitt theorem.
Multilinear almost diagonal estimates and applications
We prove that an almost diagonal condition on the (m + 1)-linear tensor associated to an m-linear operator implies boundedness of the operator on products of classical function spaces. We then provide applications to the study of certain singular integral operators.
Multilinear operators on spaces
Given Banach spaces , and a compact Hausdorff space , we use polymeasures to give necessary conditions for a multilinear operator from into to be completely continuous (resp. unconditionally converging). We deduce necessary and sufficient conditions for to have the Schur property (resp. to contain no copy of ), and for to be scattered. This extends results concerning linear operators.
Multiple summing operators on spaces
We use the Maurey-Rosenthal factorization theorem to obtain a new characterization of multiple 2-summing operators on a product of spaces. This characterization is used to show that multiple s-summing operators on a product of spaces with values in a Hilbert space are characterized by the boundedness of a natural multilinear functional (1 ≤ s ≤ 2). We use these results to show that there exist many natural multiple s-summing operators such that none of the associated linear operators is s-summing...
On multilinear generalizations of the concept of nuclear operators
This paper introduces the class of Cohen p-nuclear m-linear operators between Banach spaces. A characterization in terms of Pietsch's domination theorem is proved. The interpretation in terms of factorization gives a factorization theorem similar to Kwapień's factorization theorem for dominated linear operators. Connections with the theory of absolutely summing m-linear operators are established. As a consequence of our results, we show that every Cohen p-nuclear (1 < p ≤ ∞ ) m-linear mapping...
Point fixe d'une application non contractante.
We study a multilinear fixed-point equation in a closed ball of a Banach space where the application is 1-Lipschitzian: existence, uniqueness, approximations, regularity.
Representation of multilinear operators on C(K, X) spaces.
We present a Riesz type representation theorem for multilinear operators defined on the product of C(K,X) spaces with values in a Banach space. In order to do this we make a brief exposition of the theory of operator valued polymeasures.
Some properties of -convexity.
Some properties of regular bilinear operators.
Tensor norms related to the space of Cohen p-nuclear multilinear mappings.
The inclusion theorem for multiple summing operators
We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.
The symmetric tensor product of a direct sum of locally convex spaces
An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology τ such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for gives a direct proof of a recent result of Díaz and Dineen (and generalizes it to other topologies τ) that the n-fold projective symmetric and the n-fold projective “full” tensor product of a locally convex space E are isomorphic if E is isomorphic to its square .
The trace class is a -algebra.
Vector and operator valued measures as controls for infinite dimensional systems: optimal control
In this paper we consider a general class of systems determined by operator valued measures which are assumed to be countably additive in the strong operator topology. This replaces our previous assumption of countable additivity in the uniform operator topology by the weaker assumption. Under the relaxed assumption plus an additional assumption requiring the existence of a dominating measure, we prove some results on existence of solutions and their regularity properties both for linear and semilinear...
Weighted boundedness for multilinear Marcinkiewicz operators on some Hardy spaces