Vector Measures, c₀, and (sb) Operators

• Autorzy: Elizabeth M. Bator , Paul W. Lewis , Dawn R. Slavens
• Języki publikacji: EN

Abstrakty

EN

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 dealing with unconditionally converging operators. A characterization of the existence of a countably additive, non-strongly bounded representing measure in terms of c₀ is presented. This characterization resolves a question posed in 1970.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 28B05: Vector-valued set functions, measures and integrals
• 46B28: Spaces of operators; tensor products; approximation properties
• 46G10: Vector-valued measures and integration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2006
• Tom: 54
• Numer: 1
• Strony: 63-73

Daty

wydano

2006

Twórcy

autor

Elizabeth M. Bator

• Department of Mathematics, University of North Texas, Denton, TX 76203-1430, U.S.A.

autor

Paul W. Lewis

• Department of Mathematics, University of North Texas, Denton, TX 76203-1430, U.S.A.

autor

Dawn R. Slavens

• Department of Mathematics, Midwestern State University, Wichita Falls, TX 76308, U.S.A.

Identyfikatory

DOI

10.4064/ba54-1-6