Journal article
Archimedes integrals and conuclear spaces
Journal of the Australian Mathematical Society, Vol.47(01), pp.22-31
1989
Abstract
The lack of completeness with respect to the semivariation norm, of the space of Banach space valued functions, Pettis integrable with respect to a measure μ, often impedes the direct extension of results involving integral representations, true in the finite-dimensional setting, to the general vector space setting. It is shown here that the space of functions with values in a space Y, μ-Archimedes integrable in a Banach space X embedded in Y, is complete with respect to convergence in semivariation, provided the embedding from X into Y is completely summing. The result is applied to the case when Y is a conuclear space, in particular, when X is a function space continuously included in a space of distributions. 1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): Primary 38 B 05, 46 G 10; secondary 47 B 10, 46 A 12.
Details
- Title
- Archimedes integrals and conuclear spaces
- Authors/Creators
- B. Jefferies (Author/Creator)S. Okada (Author/Creator)
- Publication Details
- Journal of the Australian Mathematical Society, Vol.47(01), pp.22-31
- Publisher
- Cambridge University Press
- Identifiers
- 991005540383407891
- Copyright
- © 1989, Australian Mathematical Society.
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Journal article
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- Citation topics
- 9 Mathematics
- 9.50 Applied Statistics & Probability
- 9.50.1224 Banach Space
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- Mathematics
- Statistics & Probability
- ESI research areas
- Mathematics