Projective boundedness and convolution of Fréchet measures

Abstract

Fréchet measures of order n n ( F n \mathcal {F}_n -measures) are the measure- theoretic analogues of bounded n n -linear forms on products of C 0 ( K ) C_0(K) spaces. In an LCA setting, convolution of F 2 \mathcal {F}_2 -measures is always defined, while there exist F 3 \mathcal {F}_3 -measures whose convolution cannot be defined. In a three-dimensional setting, we demonstrate the existence of an F 2 \mathcal {F}_2 -measure which cannot be convolved with arbitrary F 3 \mathcal {F}_3 -measures.