{mutlak olmayan tipten $\ell (\widetilde {B},p)$ dizi uzayi ve bazi geometrik özellikleri

This master thesis consists of six chapters. In the introductory chapter of the thesis, preliminary information is briefly given about the purpose of this study after mentioning various band matrices. The second chapter is devoted to the collecting sequence space and all the fundamental concepts which are frequently used in this thesis. In the third chapter, after the definition of the matrix domain, the literature search of the matrix domain is described in detail. Moreover, the linear sequence space ℓ(B,p) is defined and proved that it is a complete paranormed space with a Schauder basis. In the fourth chapter, two different situations of the sequence p=(p_{k}) are taken into consideration and alpha-, betha- and gamma- duals of the sequence space ℓ(B,p) are determined by means of some given lemmas. In the fifth chapter, the classes (ℓ(B,p),ℓ_{∞}), (ℓ(B,p),f), (ℓ(B,p),c) and (ℓ(B,p),c₀) of infinite matrices are characterized. In addition to those, the charac- terizations of some other classes of matrix transformations from the space ℓ(B,p) to the Euler, Riesz, difference; and so forth sequence spaces are found out using some presented lemmas. In the sixth chapter, constituting the main body of the thesis, the geometric properties of the non-absolute space ℓ(B,p) such as rotundity, and Kadec-Klee and uniform Opial ones are investigated.