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N Ghoussoub 《Journal of multivariate analysis》1979,9(1):173-178
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. 相似文献
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N Ghoussoub 《Journal of multivariate analysis》1979,9(1):165-172
We extend the notion of real-valued asymptotic martingales to the Banach lattice valued case. Unlike the other extensions, the notion of “orderamart” preserves the lattice property of real amarts. We show also, a Riesz decomposition, a weak and strong convergence theorem, a probabilistic characterization of A-L spaces from which we can prove that a Banach lattice with the shur property and a quasi-interior point in the dual is an l1(Γ). 相似文献
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