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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3523-3528
- MSC (1991): Primary 43A05, 46A32
- DOI: https://doi.org/10.1090/S0002-9939-00-05439-3
- MathSciNet review: 1690976