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Monotone Semigroups of Operators on Cones*

Published online by Cambridge University Press:  20 November 2018

David W. Boyd
David W. Boyd*
Affiliation:
California Institute of Technology
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In this paper we consider a special class of linear operators defined on a cone K in a Banach space X. This class of operators is the natural generalization of a class of operators which has applications in the theory of interpolation spaces. In particular, using the criteria developed in Theorem 1, it is possible to characterize those sequence spaces X such that every linear operator A of weak types (p, p) and (q, q) is a continuous mapping of X into itself. For details of this we refer the reader to [3].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 3 , June 1969 , pp. 299 - 309
Copyright
Copyright © Canadian Mathematical Society 1969

Footnotes

*

This work was supported in part by N. S. F. grant G. P. 6111.

References

1. Bonsall, F. F., Linear operators in complete positive cones. Proc. Lond. Math. Soc. 8 (1958) 53–75.Google Scholar
2. Boyd, D. W., The spectral radius of averaging operators. Pac. J. Math. 29 (1968) 79–95.Google Scholar
3. Boyd, D. W., Indices of function spaces and their relationship to interpolation. Canad. J. Math, (to appear).Google Scholar
4. Hille, E. and Phillips, R.S., Functional analysis and semigroups. (Providence, 1957).Google Scholar
5. Kelley, J. L. and Namioka, I. et al, Linear topological spaces. (Van Nostrand, Princeton, 1963).Google Scholar
6. Luxemburg, W.A.J., Banach function spaces. (Thesis, Delft Technical University, 1955).Google Scholar