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Vector Measures, c₀, and (sb) Operators

Elizabeth M. BatorPaul W. LewisDawn R. Slavens — 2006

Bulletin of the Polish Academy of Sciences. Mathematics

Emmanuele showed that if Σ is a σ-algebra of sets, X is a Banach space, and μ: Σ → X is countably additive with finite variation, then μ(Σ) is a Dunford-Pettis set. An extension of this theorem to the setting of bounded and finitely additive vector measures is established. A new characterization of strongly bounded operators on abstract continuous function spaces is given. This characterization motivates the study of the set of (sb) operators. This class of maps is used to extend results of P. Saab...

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