On Weakly Measurable Stochastic Processes and Absolutely Summing Operators
نویسنده
چکیده
A linear and continuous operator between Banach spaces is said to be absolutely summing if it maps unconditionally convergent series into absolutely convergent series. Moreover, it improves properties of stochastic processes. Indeed, N.Ghoussoub in [7] proved that an operator is absolutely summing if and only if it maps amarts (asymptotic martingales) into uniform amarts. In this paper we go a bit further studying the composition of stochastic processes consisting of weakly measurable functions with absolutely summing operators. In particular, we consider stochastic processes of McShane and Pettis integrable functions. Both these processes generalize the more familiar notion of Bochner stochastic processes. For functions taking values in an infinite dimensional Banach space the Bochner integral and the Pettis integral are the most known generalizations of the Lebesgue integral. The family of all McShane integrable functions is strictly contained between the family of all
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