The order completeness of some spaces of vector-valued functions

1 August 1974

journal article
research article
Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society

Vol. 11 (1) , 57-61
https://doi.org/10.1017/s000497270004363x

Abstract

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.

Keywords

ORDER COMPLETENESS
SUFFICIENT
SPACES OF VECTOR
VECTOR VALUED FUNCTIONS
COMPACT
BANACH

This publication has 4 references indexed in Scilit:

Measures on F-Spaces
Transactions of the American Mathematical Society, 1968
On characterizing Köthe sequence spaces as vector lattices
Mathematische Annalen, 1967
A note concerning certain product spaces
Archiv der Mathematik, 1960
Produits tensoriels topologiques et espaces nucléaires
Memoirs of the American Mathematical Society, 1955