Archimedes integrals and conuclear spaces

Journal of the Australian Mathematical Society

B. Jefferies¹ 

[1] S. Okada

关键词: primary 38 B 05;    46 G 10;    secondary 47 B 10;    46 A 12;   

DOI  :  10.1017/S1446788700031165

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

Unknown