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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



$o$-weakly compact mappings of Riesz spaces

Author: P. G. Dodds
Journal: Trans. Amer. Math. Soc. 214 (1975), 389-402
MSC: Primary 47B55; Secondary 46E40
MathSciNet review: 0385629
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Abstract: A characterization is given of linear mappings from a Riesz space to a Banach space which map order intervals to relatively weakly compact sets. The characterization is based on recent results of Burkinshaw and Fremlin. A number of applications are made to known results concerning weakly compact mappings and to results in the theory of Banach space-valued measures.

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Keywords: Riesz spaces, locally <I>s</I>-bounded vector measures, disjoint sequences, <IMG WIDTH="55" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img4.gif" ALT="$C(K)$"> operator theory
Article copyright: © Copyright 1975 American Mathematical Society