本論文在於探討定義在不同的序列空間(c0、c、l1、lp)的加權複合算子，其為緊緻的充分必要條件為何。我們先於c0空間的情形，得到加權複合算子成為緊緻算子、弱緊緻算子或完全連續算子的充分必要條件及其他一些結果。接著，這些結果被推廣到c、l1、lp(1<p<∞)等空間的情形。最後，我們得到了從c0、c、lp映射到c0、c、lq之間的加權複合算子成為緊緻算子、弱緊緻算子或完全連續算子的條件及彼此間的關係。

In this thesis, we study weighted composition operatorsT(xn)=(λnXσ(n)) between sequence spaces(c0,c,l1,lp), and more precisely, the sufficient and necessary condition that they are compact. First,we obtain some results of weighted composition operators beingcompact, weakly compact and completely continuous on c0 spaces. Then, we extend then to c,l1,and lp(1<p<∞) spaces. Finally, we obtain the condition that an operator from c0, c or lp into c0, c, or lq is compact, weakly compact or completely continuous.

(1)Introduction......................................................3
(2)Preliminaries.....................................................4
(3)Multiplication operators of c0 and c..............................7
(4)Multiplication operators of l1...................................12
(5)Multiplication operators of lp (1<p<∞)..........................14
(6)Weighted composition operators...................................16
(7)Bounded linear operators between different sequence spaces.......17
Reference...........................................................19

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