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Lp Spaces from Matrix Measures: A Correction and their Interpolation

Published online by Cambridge University Press:  20 November 2018

Patrick J. Browne  and
Claude Costa
Patrick J. Browne
Affiliation:
Department of Mathematics and Statistics, The University of CalgaryCalgary, Alberta, Canada
Claude Costa
Affiliation:
Department of Mathematics and Statistics, The University of CalgaryCalgary, Alberta, Canada
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Abstract

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We discuss the construction of the spaces Lp(μij), 1 ≤ p ≤ ∞, where {μij} is an n × n positive matrix measure, correct a mistake in the literature concerning those spaces and develop an interpolation theory for them.

Keywords

46E30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 2 , 01 June 1983 , pp. 137 - 143
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Bergh, J. and Löfström, J., Interpolation Spaces, Springer-Verlag, , New York, 1976.Google Scholar
2. Binding, P. and Browne, P. J., Lp spaces from matrix measures, Canad. Math. Bull, 18, (1975), 19–26.Google Scholar
3. Costa, C., Interpolation of Matrix Measure Function Spaces, M.Sc. Thesis, University of Calgary, 1981.Google Scholar
4. Dunford, N. and Schwartz, J. T., Linear Operators, Part II, Wiley-Interscience, New York, 1963.Google Scholar
5. Triebel, H., Interpolation Theory, Function Spaces, Differential Operators, North Holland, New York, 1978.Google Scholar