Study On Infinite Matrix Transformation Of Operator

Infinite matrix theory is one the important subjects of calculus. The general theory of infinite matrix has been studied for 90 years, since the famous regular theory of Silverman- Toeplitz as founded in 1911. The decisive breakthrough in research of infinite matrix transformation is that the action of continuous linear operators in Banach Space on vector sequence, which was started at 1950 by A.Robinson .After that, we have acquired many results in summability theory of continuous linear operator in Banach Space .In 1993, professor Li RongLu broke out the linearity constraints on operators and succeeded in getting the marked improvement of Maddox-Swartz theorem.In this paper, firstly, we make a systematic statement of infinite matrix transformation; Secondly, we make a conclusion the characteristic of infinite matrix family which are made up by continuous tinear operators. Thirdly, enlarge the conditions of operators, we get a family A _? ( X , Y), which is called absorbing operators family, it concludes all of the linear , all of the homogeneous operators and more nonlinear operators. Further, make use of Junde Wu , result of the equivalent of the basic matrix theory and uniform convergent principle, We studied the characters of matrix families(c₀ ( X ), l^∞( I , Y)),(c(X), l^∞(I,Y)) and (l^∞(X),l^∞(I,Y)),those matrix families are made up of absorbing operators; Finally, we searched for the action of matrixs (T_αj )_{α∈I ,j∈N}, composed of maps in R_(?),U ( X , Y),on vector sequence. At last, we have described the qualities of the class (l^∞( X ), l^∞( I , Y))= ( c₀ ( X ), l^∞( I , Y))...