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Products of a C-Measure and a Locally Integrable Mapping

Published online by Cambridge University Press:  20 November 2018

Marston Morse  and
William Transue
Marston Morse
Affiliation:
Institute for Advanced Study Princeton, New Jersey
William Transue
Affiliation:
Kenyon College Gambier, Ohio
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Let C be the field of complex numbers and E a locally compact topological space. The authors' theory of C-bimeasures Λ and their Λ-integrals in (1; 2) leads to integral representation of bounded operators from A to B' where A and B are MT-spaces as defined in (3). These MT-spaces include the -spaces and Orlicz spaces as special cases.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 475 - 486
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Morse, M. and Transue, W., C-imeasures Λ and their superior integrals, Rend. Circ. Mat, Palermo, 4 (1955), 270–300.Google Scholar
2. Morse, M. and Transue, W., C-bimeasures Λ and their integral extensions, Ann. Maths., 64 (1956), 480–504.Google Scholar
3. Morse, M. and Transue, W., Semi-normed vector spaces with duals of integral type, J. d'Analyse Math., 4 (1955), 149–186.Google Scholar
4. Morse, M. and Transue, W., Vector subspaces A of CE with duals of integral type, J. Math. Pures Appl., 00 (1957), to be published.Google Scholar
5. Morse, M. and Transue, W., A comparison of two theorems on integration, Proc. Nat. Acad. Sci., 00 (1957), to be published.Google Scholar
6. Bourbaki, N., Éléments de Mathématique, 8, Topologie Générale, Chap. IX (Paris, 1948).Google Scholar
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8. Bourbaki, N., Éléments de Mathématique, 21, Intégration, Chap. V (Paris, 1956)Google Scholar