Since nonlinear schur theorem was proposed, it broke the limitation of linear operator matrices. And in this paper we study the summability theory for a class of matrices of nonlinear mapping, and the characterizations of a class of infinite matrix transformations are obtained. These results enrich the results on infinite matrices transformations, and have important meaning for the study of Banach space.
Bani-Ahmad, F.A. and Bani-Domi, W. (2016) New Norm Equalities and Inequalities for Operator Matrices. Journal of Inequalities and Applications, 2016, Article number: 175. https://doi.org/10.1186/s13660-016-1108-y
Li, R.L., Kang, S.M. and Swartz, C. (2002) Operator Matrices on Topological Vector Spaces. Journal of Mathematical Analysis and Applications, 274, 645-658.