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The order completeness of some spaces of vector-valued functions

Published online by Cambridge University Press:  17 April 2009

Donald I. Cartwright
Donald I. Cartwright
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA.
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Abstract

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Let E be a Banach lattice. Necessary and sufficient conditions are given for the order completeness of the Banach lattices C(X, E) and L1(μ, E) in terms of the compactness of the order intervals in E. The results have interpretations in terms of spaces of compact and nuclear operators.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 1 , August 1974 , pp. 57 - 61
Copyright
Copyright © Australian Mathematical Society 1974

References

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