This is an announcement for the paper "Coincidence of extendible vector-valued ideals with their minimal" by Daniel Galicer and Roman Villafane.

Abstract: We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if $\mathfrak A$ 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. Similar statements are given for ideals of vector-valued homogeneous polynomials. For our purposes we also establish a vector-valued version of the Littlewood-Bogdanowicz-Pe{\l}czy'nski theorem, which we believe is interesting in its own right.

Archive classification: math.FA

Mathematics Subject Classification: 46G25, 46B22, 46M05, 47H60

Remarks: 25 pages

Submitted from: dgalicer@dm.uba.ar

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1401.7896

or

http://arXiv.org/abs/1401.7896