Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-23T01:28:20.274Z Has data issue: false hasContentIssue false
  • English
  • Français

On the MT*- and λ-Conjugates of Spaces

Published online by Cambridge University Press:  20 November 2018

H. W. Ellis
H. W. Ellis*
Affiliation:
Queen's University Kingston
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Marston Morse and William Transue (9, 10), motivated by their theory of bilinear functions, introduced and studied vector function spaces called MT-spaces for which each element of the dual is represented by an integral with respect to a suitable (C) measure. In this paper the definition of real MT-spaces is generalized to give spaces, called MT*-spaces, for which part but not all of the dual is of integral type and this part is called the MT*-conjugate of the space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 381 - 391
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Banach, S., Théorie des opérations linéaires (Warsaw, 1932).Google Scholar
2. Birkhoff, G., Lattice Theory, Am. Math. Soc. Colloquium Publications, vol. XXV (New- York, 1948).Google Scholar
3. Bourbaki, N., Eléments de Mathématique, Livre VI, Integration, chaps. I-IV (Paris, 1952).Google Scholar
4. Bourbaki, N., Eléments de Mathématique, Livre VI, Integration, chap. V (Paris, 1956).Google Scholar
5. Edwards, R. E., A theory of Radon measures on locally compact spaces, Acta. Math., 89 (1953), 133–164.Google Scholar
6. Ellis, H. W. and Halperin, I., Function spaces determined by a levelling length function, Can. J. Math., 5 (1953), 576-592.Google Scholar
7. Halperin, I. and Luxemburg, W. A. J., Reflexivity of the length function, Proc. Amer. Math. Soc, 8 (1957), 496-9.Google Scholar
8. Morse, M. and Transue, W., Products of a C-measure and a locally integrable mapping, Can. J. Math., 9 (1957), 475-486.Google Scholar
9. Morse, M., Semi-normed vector spaces with duals of integral type, J. d'Analyse Math., 4(1954-5), 149-186.Google Scholar
10. Morse, M., Vector subspaces A of CE with duals of integral type, J. Math, pures et appl., to appear.Google Scholar
11. Yosida, K. and Hewitt, E., Finitely additive measures, Trans. Amer. Math. Soc, 72 (1952), 46-66.Google Scholar