Coincidence of extendible ideals with their minimal kernel

ROMÁN VILLAFAÑE; DANIEL GALICER

Buenos Aires

Workshop; Worksop on infinite dimensional analysis Buenos Aires 2014; 2014

CONICET - UBA - Universidad de San Andres - Universidad Torcuato Di Tella

We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if $\U$ is an ideal of $n$-linear mappings we give conditions for which the following equality $\mathfrak A(E_1,\dots,E_n;F) = {\mathfrak A}^{min}(E_1,\dots,E_n;F)$ holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis on the space $\mathfrak A(E_1,\dots,E_n;F)$. Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where $\mathfrak A$ is the classical ideal of extendible or Pietsch-integral multilinear operators. Joint work with Daniel Galicer.