Summability and vector amarts

N. Ghoussoub

Journal of Multivariate Analysis, 1979, vol. 9, issue 1, 173-178

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.

Keywords: Amarts; uniform; amarts; strong; potentials; absolutely; summing; operators; Ricsz; spaces (search for similar items in EconPapers)
Date: 1979
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