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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Email: Blei@uconnvm.uconn.edu

J. Caggiano
Affiliation: Department of Mathematics & Computer Science, Arkansas State University, Box 70, State University, Arkansas 72467
Email: Caggiano@csm.astate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05439-3
PII: S 0002-9939(00)05439-3
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