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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

[1]Curtis, Philip C. Jr, “A note concerning certain product spaces”, Arch. Math. 11 (1960), 50–52.Google Scholar
[2]Dunford, Nelson and Schwartz, Jacob T., Linear operators, Part I (Interscience [John Wiley & Sons], New York, London, 1958).Google Scholar
[3]Grothendieck, A., Produits tensoriels topologiques et espaces nucléaires (Mem. Amer. Math. Soc. 16. Amer. Math. Soc., Providence, Rhode Island, 1955).Google Scholar
[4]Lotz, Heinrich P., “Minimal and reflexive Banach lattices”, Math. Ann. (to appear).Google Scholar
[5]Peressini, Anthony L., Ordered topological vector spaces (Harper & Row, New York, Evanston, and London, 1967).Google Scholar
[6]Seever, G.L., “Measures on F-spaces”, Trans. Amer. Math. Soc. 133 (1968), 267–280.Google Scholar
[7]Semadeni, Z., Banach spaces of continuous functions (Warsaw, 1971).Google Scholar
[8]Walsh, Bertram, “On characterizing Köthe sequence spaces as vector lattices”, Math. Ann. 175 (1968), 253–256.Google Scholar