Some sequence spaces and basis types

The first part of the thesis, which consists of five parts, is devoted to the historical development of the subject and the necessary literature. In the second chapter, necessary basic concepts and theorems of functional analysis and topology are given for the next chapters. In the third chapter, the concepts of basis and basic sequences given for Banach spaces are given and the equivalence of bases and basic sequences is examined. The proof of the Eberlein-Smulian Theorem is given as an application of basic sequences. In the fourth chapter, (1≤ p < 1) is divided into isomorphic and complementary subspaces of Banach spaces 𝓁p and c0. In the fifth chapter, unconditional, shrinking and boundedly complete basis types of Banach spaces are examined. KEYWORDS: Banach space, Sequence space, Basis, Schauder basis, Basic sequence, Unconditional basis, Shrinking basis, Boundedly complete basis