On the subspace of the domain of matrix

The present thesis consists of five chapters. In the first chapter, brief history of K- and FK-spaces and general knowledge were given.In the second chapter, for understand other chapters some basic definitions and theorems and basic concepts such as topological space, locally convex space and sequence spaces were mentioned. In the third chapter, some subspaces of K- and FK-spaces were examined by section operators. Using the properties of these subspaces, relation among the dualspaces were given.In the fourth chapter, some subspaces of the matrix domain were investigated.In the fiveth chapter, some subspaces of the special matrix (such as Ces`aro,Zweier and Difference) domain were investigated. KEYWORDS: Sequence space, K-space, FK-space, AK, AB, SAK, FAK and AD property, Matrix domain, Convergence domain.