Coincidence of extendible vector-valued ideals with their minimal kernel

GALICER DANIEL; VILLAFAÑE ROMAN

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2015 vol. 421 p. 1743 - 1766

0022-247X

We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if Ais an ideal of n-linear mappings we give conditions for which theequality A(E1, ..., En; F) =Amin(E1, ..., En; F) holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis of the space A(E1, ..., En; F). Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where Ais the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials.