Projective boundedness and convolution of Fréchet measures

Blei, R.; Caggiano, J.

doi:10.1090/S0002-9939-00-05439-3

Projective boundedness and convolution of Fréchet measures
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by R. Blei and J. Caggiano PDF

Proc. Amer. Math. Soc. 128 (2000), 3523-3528 Request permission

Abstract:

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

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