Ideal convergence and Ideal Dunford integration on Banach space.

Abstract

In this paper, we propose on type of Dunford integration in the concept of ideal convergence This wants to construct a new convergence of functions in Banach space to definite the measurable functions. The main result is construction on the type of Dunford as the Ideal integral. Ideal Dunford integral is an application of the convergence ideal in integration but weak integration. For this been followed the usual route by first introducing the ideal Dunford integral and demonstrating for the ideal Dunford integral the most important statements related to it in the classical case. In this paper, we prove if the function f is Dunford integrable then it is ideal Dunford integrable, but conversely, this is not true. This gives the meaning of the extension of Dunford integration in our article. We are motivated by this by one important example published by Schvabik and Guoju, [20].