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Summability and vector amarts

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  • Ghoussoub, N.

Abstract

We show that an operator is absolutely summing if and only if it maps amarts into uniform amarts, from which we can deduce a theorem of A. Bellow and another of Edgar-Sucheston. We also show that the absolute value of a Banach lattice valued potential is a potential if and only if the lattice is an A-M space from which we deduce that the L1-bounded amarts form a Ricsz space if and only if the space is finite dimensional.

Suggested Citation

  • Ghoussoub, N., 1979. "Summability and vector amarts," Journal of Multivariate Analysis, Elsevier, vol. 9(1), pages 173-178, March.
    • Handle: RePEc:eee:jmvana:v:9:y:1979:i:1:p:173-178
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