Generalized difference sequence spaces and their dual spaces

ABSTRACTMsSc ThesisGENERALIZED DIFFERENCE SEQUENCE SPACES AND THEIR DUALSPACESGülhan ÇAKMAKAfyon Kocatepe UniversityGraduate School of Natural and Applied SciencesDepartment of MathematicSupervisor: Prof. Dr. Fatih NURAYThis thesis consists of six chapters. The first chapter is the introduction of the thesis. Inthis chapter, there is given some short information about the subject of the thesis. In thesecond chapter, all the necessary definitions and basic theorems fort his study havebeen given. In the third chapter, bounded, convergent and the null sequence spaces aregeneralized to ∆ -sequence spaces and defined their duals spaces. Necessary andsufficient conditions are given for an infinite A matrix to map between these dualspaces and ∆ -sequence spaces. In the fourth chapter, these ∆ -sequence spaces aregeneralized again to ∆2 -sequence spaces and given their dual spaces. Furthermorenecessary and sufficient conditions are determined for an infinite A matrix to mapbetween the difference sequence spaces and ∆2 -sequence spaces. In the fifth chapter,∆2 -sequence spaces are generalized for a ?m? positive integer and defined ∆m -sequence spaces and given their dual spaces. Necessary and sufficient conditions aregiven for an infinite A matrix to map between the sequence spaces which are defined inthe chapter third,fourth and fifth. In the sixth chapter, ∆m -sequence spaces aregeneralized for any fixed v = v(k ) sequence which is a sequence of non-zero compleksnumbers and obtained ∆m -sequence spaces. The duals of these ∆m -sequence spacesv vand matrix maps are given.June 2007, 56 pageKeywords: Difference sequence spaces, α-, β-, γ- and continous dual spaces, matrixmapsiii