On unconditionally convergent series in normed spaces

The first part of the study, which consists of five chapters, is devoted to the historical development of the subject and the literature on the subject. In the second chapter, the basic concepts and theorems of functional analysis required for the next chapters are discussed. In the third chapter, the series, bases and fundamental sequences, which form the basis of this study, are discussed. Characterization of Banach spaces containing copy and complementary copy of the sequence space $c_0$ is given. The original chapters of the thesis are the fourth and fifth chapters. In the fourth chapter, the sequence space $Ces_0$ is introduced and some of its properties are examined. In the fifth chapter, it is shown that the basis of the space $Ces_0$ forms an unconditionally convergent series. Then, some properties of certain linear transformations defined on $Ces_0$ are characterized with the help of unconditionally Cauchy and unconditionally convergent series.