Orlicz-Pettis Theorem And Operator Series Multiplier Convergent

This thesis investigates the Orlicz-Pettis theorem and invariant theorem in general dual system,seeking new full invariant result,etc.Chapter1.Introduction.We present study history of the invariant theory in linear dual system and the operator series theory.Chapter2.General Orlicz-Pettis theorem.First,We present the concept of G—Valued duality pair and a recent general Orlicz-Pettis theorem.Then,We give two examples of the application of the general Orlicz-Pettis theorem.Chapter3.Invariant theorem of the operator series multiplier convergent. Using operator series multiplier convergent,AK-space of concept ,we obtained the theorem of operator series multiplier convergent invariant and the old theorem of general series multiplier convergent invariant is looked as special case.