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Projective boundedness and convolution of Fréchet measures

Authors: R. Blei and J. Caggiano
Journal: Proc. Amer. Math. Soc. 128 (2000), 3523-3528
MSC (1991): Primary 43A05, 46A32
Published electronically: June 7, 2000
MathSciNet review: 1690976
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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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Additional Information

R. Blei
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269

J. Caggiano
Affiliation: Department of Mathematics & Computer Science, Arkansas State University, Box 70, State University, Arkansas 72467

Received by editor(s): September 1, 1998
Received by editor(s) in revised form: January 28, 1999
Published electronically: June 7, 2000
Additional Notes: The first author was supported by an NSA grant
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society