S-Multiplicator Convergence On Operators Space

This thesis consists of three chapters.It investigates mainly s-multiplicator con-vergence on operators space.In chapter one,we introduce the matrix theorem research background,enumeratethe basic concepts and the theorems about topological group, compatible topology ondual space,admissible polar topology and so on,and review the recent years matrixapplication theorem development present situation.Second chapter we mainly discuss center the sufficiency and the essential con-dition that the s-multiplicator convergence becomes full invariance on the operatorspace.From this,we proved that c0(l~p, 1≤p≤∞)-multiplicator convergence is fullinvariance.Third chapter we obtained some conclusion when every Ei on product space iscompact set and found the relation between s-multiplicator weakedσF convergenceand s-multiplicator F uniformly convergence.