Convolution factorability of bilinear maps and integral representations

Integral representation of product factorable bilinear operators and summability of bilinear maps on C(K)-spaces

“…As in the pointwise-product case, this can be improved if we consider the zero product preservation. In this case, φ factors through L 1 pTq by convolution as φ T ¥ ¦ c (see [17,Theorem 3.4]). Thus, there is a functional in pL 1 pTqq ¦ -that is, a function h L V pTqsuch that φpf, gq…”

“…The main reference, that provides the starting point of our analysis, is the space of Grothendieck's integral bilinear forms, that gives an isometric representation of the dual of the injective tensor product (see for example [14,Ch.4]). Zero product preserving bilinear operators and convolution-orthogonal polynomials, which are defined using convolution in Lebesgue spaces of locally compact groups, define other class of examples that fits with our procedure (see [2,1,3,17] and the references therein). Some classical constructions with spaces of operators can also be adapted to our setting, using for example the so called trace duality.…”

Convolution-factorable multilinear operators

“…The purpose of this paper is to present a generalization for n-linear operators of the factorization given in [15] motivated by the convolution of three functions 104 EZG İ ERDO GAN introduced by Arregui and Blasco in [4]. Although the main theorem is similar to the bilinear case, completely new results are given and different applications are presented.…”

Product factorable multilinear operators defined on sequence spaces

“…Recently, the author together with other mathematicians have investigated the class of multilinear operators acting in the topological product of Banach function spaces and integrable functions factoring through the pointwise product and the convolution operation, respectively (see [12][13][14]). Motivated by these ideas, in this paper we introduce the notion of product factorability for multilinear operators de…ned on topological products of spaces of (scalar) p-summable sequences, and we prove that this class coincides with the class of zero product preserving multilinear maps.…”