Dérivation de mesures à valeurs vectorielles
Let E be a Banach space with 1-unconditional basis. Denote by (resp. ) the main diagonal space of the n-fold full (resp. symmetric) projective Banach space tensor product, and denote by (resp. ) the main diagonal space of the n-fold full (resp. symmetric) projective Banach lattice tensor product. We show that these four main diagonal spaces are pairwise isometrically isomorphic, and in addition, that they are isometrically lattice isomorphic to , the completion of the n-concavification of...
Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for -triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems.