Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T20:44:53.388Z Has data issue: false hasContentIssue false
  • English
  • Français

Lp Spaces Generated by Certain Operator Valued Measures

Published online by Cambridge University Press:  20 November 2018

Paul Binding  and
Patrick J. Browne
Paul Binding
Affiliation:
Department of Mathematics and Statistics, The University of Calgary, Calgary, Alberta, CanadaT2N 1N4
Patrick J. Browne
Affiliation:
Department of Mathematics and Statistics, The University of Calgary, Calgary, Alberta, CanadaT2N 1N4
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.

In this paper we investigate the structure of certain spaces of operator valued measures and the Lp spaces they generate. The work is motivated by our earlier paper [1] in which we studied the Lp spaces generated by matrix valued measures. The present results can thus be regarded as a generalization of this “finite dimensional” situation.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 4 , 01 December 1976 , pp. 403 - 416
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Binding, P. and Browne, P. J., LP Spaces from Matrix Measures, Canad. Math. Bull., 18 (1975), 19–26.Google Scholar
2. Day, M. M., Some More Uniformly Convex Spaces, Bull. Amer. Math. Soc. 47 (1941), 504–507.Google Scholar
3. Dinculeanu, N., Vector Measures, Pergamon Press, London, 1967.Google Scholar
4. Dixmier, J., Les fonctionnelles linéaires sur l’ensemble des opérateurs bornés d’un espace de Hilbert, Ann. of Math. (2), 51 (1950), 387–408.Google Scholar
5. Dunford, N. and Schwartz, J. T., Linear Operators, Part I: General Theory, Part II: Spectral Theory, Interscience Publishers, New York, 1963.Google Scholar
6. Hanner, O., On the Uniform Convexity of LP and lp , Ark. för Mat., 3 (1956), 239–244.Google Scholar
7. Kuratowski, K. and Ryll-Nardzewski, C., A General Theorem on Selectors, Bull. Acad. Polon. Sci. Ser. Mat. Astronom. Phys., 13 (1965), 397–403.Google Scholar
8. Phillips, R. S., On Weakly Compact Subsets of a Banach Space, Amer. J. Math., 65 (1943), 108–136.Google Scholar
9. Moedomo, S. and Uhl, J., Radon-Nikodỳm Theorems for the Bochner and Pettis Integrals, Pacific J. Math., 38 (1971), 531–536.Google Scholar
10. Thomas, E., The Lebesgue-Nikodỳm Theorem for Vector Valued Radon Measures, Memoirs Amer. Math. Soc. No. 139, 1974.Google Scholar
11. Titchmarsh, E. C., Introduction to the Theory of Fourier Integrals, Oxford, 1937.Google Scholar
12. Zaanen, A. C., Integration, North Holland Publishing Company, Amsterdam, 1967.Google Scholar