A decomposition of bounded scalarly measurable functions taking their ranges in dual Banach spaces

Bator, Elizabeth M.

doi:10.1090/S0002-9939-1988-0934855-3

A decomposition of bounded scalarly measurable functions taking their ranges in dual Banach spaces
HTML articles powered by AMS MathViewer

by Elizabeth M. Bator PDF

Proc. Amer. Math. Soc. 102 (1988), 850-854 Request permission

Abstract:

A decomposition of scalarly measurable functions taking their range in the dual of a Banach space into a Pettis integrable part and a weak* scalarly null part is introduced and analyzed.

References

Elizabeth M. Bator, Pettis integrability and the equality of the norms of the weak$^\ast$ integral and the Dunford integral, Proc. Amer. Math. Soc. 95 (1985), no. 2, 265–270. MR 801336, DOI 10.1090/S0002-9939-1985-0801336-4
Elizabeth M. Bator, Paul Lewis, and David Race, Some connections between Pettis integration and operator theory, Rocky Mountain J. Math. 17 (1987), no. 4, 683–695. MR 923739, DOI 10.1216/RMJ-1987-17-4-683
J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964

Linear operators

Robert F. Geitz, Pettis integration, Proc. Amer. Math. Soc. 82 (1981), no. 1, 81–86. MR 603606, DOI 10.1090/S0002-9939-1981-0603606-8
Robert F. Geitz, Geometry and the Pettis integral, Trans. Amer. Math. Soc. 269 (1982), no. 2, 535–548. MR 637707, DOI 10.1090/S0002-9947-1982-0637707-0
Liliana Janicka, Some measure-theoretical characterization of Banach spaces not containing $l_{1}$, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), no. 7-8, 561–565 (1980) (English, with Russian summary). MR 581552
Kazimierz Musiał, The weak Radon-Nikodým property in Banach spaces, Studia Math. 64 (1979), no. 2, 151–173. MR 537118, DOI 10.4064/sm-64-2-151-174
B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc. 44 (1938), no. 2, 277–304. MR 1501970, DOI 10.1090/S0002-9947-1938-1501970-8
Lawrence H. Riddle and Elias Saab, On functions that are universally Pettis integrable, Illinois J. Math. 29 (1985), no. 3, 509–531. MR 786735
Lawrence H. Riddle, Elias Saab, and J. J. Uhl Jr., Sets with the weak Radon-Nikodým property in dual Banach spaces, Indiana Univ. Math. J. 32 (1983), no. 4, 527–541. MR 703283, DOI 10.1512/iumj.1983.32.32038
Haskell P. Rosenthal, A characterization of Banach spaces containing $l^{1}$, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411–2413. MR 358307, DOI 10.1073/pnas.71.6.2411
Michel Talagrand, Pettis integral and measure theory, Mem. Amer. Math. Soc. 51 (1984), no. 307, ix+224. MR 756174, DOI 10.1090/memo/0307