𝑜-weakly compact mappings of Riesz spaces

Dodds, P. G.

doi:10.1090/S0002-9947-1975-0385629-1

$o$-weakly compact mappings of Riesz spaces
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by P. G. Dodds

Trans. Amer. Math. Soc. 214 (1975), 389-402

DOI: https://doi.org/10.1090/S0002-9947-1975-0385629-1

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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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Applications of a lemma of Rosenthal to vector measures and series in Banach spaces