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Article

Keywords:
Pettis integral; McShane integral; amart; uniform amart; absolutely summing operators
Summary:
A characterization of absolutely summing operators by means of McShane integrable stochastic processes is considered.
References:
[1] A. Bellow: Uniform amarts: a class of asymptotic martingales for which strong almost sure convergence obtains. Z. Wahrscheinlichkeitstheor. Verw. Geb. 41 (1978), 177–191. MR 0471065 | Zbl 0391.60005
[2] J. K. Brooks: Representations of weak and strong integrals in Banach spaces. Proc. Nat. Acad. Sci. U.S.A. 63 (1969), 266–279. MR 0274697 | Zbl 0186.20302
[3] N. Dunford, J. T. Schwartz: Linear Operators. Part I, Interscience, New York, 1958.
[4] G. A. Edgar, L. Sucheston: Stopping Times and Directed Sets. Cambridge University Press, New York, 1992. MR 1191395
[5] L. Egghe: Convergence of adapted sequences of Pettis-integrable functions. Pacific J. Math. 114 (1984), 345–366. MR 0757506 | Zbl 0514.46028
[6] D. H. Fremlin: The generalized McShane integral. Illinois J. Math. 39 (1995), 39–67. MR 1299648 | Zbl 0810.28006
[7] N. Ghoussoub: Summability and vector amarts. J. Multivariate Anal. 9 (1979), 173–178. MR 0530649 | Zbl 0407.60043
[8] R. A. Gordon: The McShane integral of Banach-valued functions. Illinois J. Math. 34 (1990), 557–567. MR 1053562 | Zbl 0685.28003
[9] Luu Dinh Quang: Convergence of Banach-space-valued martingale-like sequences of Pettis-integrable functions. Bull. Polish Acad. Sci. Math. 45 (1997), 233–245. MR 1477541 | Zbl 0892.60009
[10] V. Marraffa: A characterization of absolutely summing operators by means of McShane integrable functions. J. Math. Anal. Appl. 293/1 (2004), 71–78. MR 2052532 | Zbl 1087.47023
[11] V. Marraffa: Stochastic processes of vector valued Pettis and McShane integrable functions. Folia Mathematica 11 (2005). MR 2282634 | Zbl 1125.60040
[12] K. Musial: Martingales of Pettis integrable functions. Lect. Notes Math., Springer 794 (1980), 324–339. MR 0577981 | Zbl 0433.28010
[13] K. Musial: Topics in the theory of Pettis integration. Rend. Istit. Mat. Univ. Trieste 23 (1991), 177–262. MR 1248654 | Zbl 0798.46042
[14] J. Rodriguez: Absolutely summig operators and integration of vector-valued functions. J. Math. Anal. Appl. 316 (2006), 579–600. MR 2207332
[15] C. Swartz: Beppo Levi’s theorem for vector valued McShane integral and applications. Bull. Belg. Math. Soc. 4 (1997), 589–599. MR 1600292
[16] M. Talagrand: Pettis Integral and Measure Theory. vol. 51, Memoirs A.M.S., 1984. MR 0756174 | Zbl 0582.46049
[17] J. J. Uhl, Jr.: Martingales of strongly measurable Pettis integrable functions. Trans. Amer. Math. Soc. 167 (1972), 369–378. MR 0293708 | Zbl 0249.60025
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