Archimedes integrals and conuclear spaces
Jefferies, B. and Okada, S. (1989) Archimedes integrals and conuclear spaces. Journal of the Australian Mathematical Society, 47 (01). pp. 22-31.
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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.
|Publication Type:||Journal Article|
|Murdoch Affiliation:||School of Mathematical and Physical Sciences|
|Publisher:||Cambridge University Press|
|Copyright:||© 1989, Australian Mathematical Society.|
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