On copy of some sequence spaces in Banach spaces

This thesis consists of five chapters. In the first chapter of the thesis, it is mentioned about the importance in the literature and historical development of the subject. In the second chapter, basic concepts and theorems to be used in other chapter have been given. In the third chapter, complemented subspaces, projections, bases, basic sequences and convergence of the series that constitute the sub-structure of this work have been examined in detail. The characterization of the Banach spaces including the copy and complemented copy of the space c_0 have been given. In the last two parts, the works in vector valued Banach spaces as an application of the characterization obtained in the previous part have been given. The original results of the thesis have been given in the fourth and fifth chapters. In the fourth chapter, a characterization of Banach spaces containing the cs space have been studied. In the last chapter, by using a sequence in a normed space X and matrix domain of Cesàro summability method in l_∞ and c_0 some new sequence spaces have been introduced. Later, the completeness and barrelledness of normed space X through its weakly and weakly* unconditionally Cauchy series have been characterized.