Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T18:06:32.293Z Has data issue: false hasContentIssue false
  • English
  • Français

LP Spaces from Matrix Measures

Published online by Cambridge University Press:  20 November 2018

P. Binding  and
P. J. Browne
P. Binding
Affiliation:
Department of Mathematics, Statistics and Computing Science, The University of Calgary, Calgary Alberta T2N 1N4
P. J. Browne
Affiliation:
Department of Mathematics, Statistics and Computing Science, The University of Calgary, Calgary Alberta T2N 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.

It is known that a Hilbert space, L2(μij), can be constructed from an n × n positive matrix measure (μij), [5, pp. 1337–1346]. The aim of this note is to show that Banach spaces, corresponding to the usual LP spaces, can also be constructed and to investigate their properties.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 1 , April 1975 , pp. 19 - 25
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Clarkson, J. A., Uniformly Convex Spaces, Trans. Amer. Math. Soc, 40 (1936), 396-414.Google Scholar
2. Cudia, D. F., Rotundity, Proc. A.M.S. Symposium in Pure Mathematics, 7 ("Convexity", Copenhagen 1962), 73-97.Google Scholar
3. Day, M. M., Uniform Convexity in Factor and Conjugate Spaces, Ann. of Math., 45 (1944), 375-385.Google Scholar
4. Dinculeanu, N., Vector Measures, Pergamon Press, London 1967.Google Scholar
5. Dunford, N. and Schwartz, J. T., Linear Operators, Part II, Interscience, New York, 1963.Google Scholar