On λ-multiplier convergent series

The present thesis consists of five chapters and a reference list. In the first chapter, a brief introduction of corresponding knowledge of thesis is given. In the second chapter, some important literature which used in thesis briefly are given. In the third chapter, some materials and method which used in preparation of thesis are given. In the fourth chapter, firstly, some basic definitions, theorems and concepts which are used in other chapters of thesis, and elementary properties of sequence spaces with 0-giding hump property and the spaces of λ-multiplier convergent series, and a version of Orlicz-Pettis Theorem which is obtained from λ-multiplier convergent operator series such that λ is a sequence space with AK property are given. Finally, the relationship of a barrelled AK-space λ, the β-dual of this space λ^β and λ-multiplier convergence are examined. In the last chapter of thesis, discussion and conclusion part is reviewed.