Summability Theorem For A Class Of Matrices Of Nonlinear Mapping On Banach Spaces

This thesis consists of two chapters. At first, it presents a survey of the study history as well as present situation in the infinite matrix transformations, and then it investigates mainly the summability theory for a class of matrices of nonlinear mapping. The main results for the theory of infinite matrices transformations obtained in this paper are as follows: firstly, the new summability results for operator matrices on Banach space are obtained. Secondly, new results are established for matrices(c0(X),l(I,Y)) of linear and some nonlinear mappings between Banach spaces.These results enrich the study results on infinite matrices transformations, and have important meaning for the study of Banach space.