Vector measures, c0, and (sb) operators

• Autorzy: Bator E. M. , Lewis P. W. , Slavens D. R.
• Języki publikacji: EN

Abstrakty

EN

Emmanuele showed that if Σ is a σ-algebra of sets, Χ is a Banach space, and μ : Σ → Χ 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.

Słowa kluczowe

EN

vector measure; representing measure; strongly additive; strongly bounded; (sb) operator

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2006
• Tom: Vol. 54, no 1
• Strony: 63--73
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Bator E. M.

autor

Lewis P. W.

autor

Slavens D. R.

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

Bibliografia

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