On matrix transformations between some sequence spaces and the hausdorff measure of noncompactness

This study which is entitled ? On Matrix Transformations between Some Sequence Spaces and the Hausdorff Measure of Noncompactness? contains four chapters. In the first chapter, some basic definitions and theorems related to sequence spaces, matrix mappings and the Hausdorff measure of noncompactness are given. The second and third chapters are original parts of this study.In the second chapter, the Euler mth-order difference sequence spaces e_0^t (B^((m) )), e_c^t (B^((m) )) and e_?^t (B^((m) )) are introduced and the ?-, ß-, ?- duals of these spaces are determined. Also, some classes of matrix mappings on them are characterized. Moreover, by applying the Hausdorff measure of noncompactness, the characterization of some classes of compact operators on the sequence spaces e_0^t (B^((m) )) and e_?^t (B^((m) )) are given.In the third chapter, the weighted B-difference sequence spaces l(u,v,p;B) and l_p (u,v;B) are defined. Also, some topological properties of the paranormed space l(u,v,p;B) are studied and some classes of matrix mappings on this space are examined. Moreover, the Hausdorff measure of noncompactness is applied to characterize some classes of compact operators given by infinite matrices on the space l_p (u,v;B)(1?pKeyword: Dizi uzayları = Sequence spaces ; Hausdorff ölçüsü = Hausdorff measure ; Kompakt operatörler = Compact operators ; Matris dönüşümleri = Matrix transformations ; Schauder bazları = Schauder bases