Some generalized difference sequence spaces

SUMMARY Ph. D Thesis SOME GENERALIZED DIFFERENCE SEQUENCE SPACES Çiğdem BEKTAŞ Fırat University Graduate School of Natural and Applied Sciences Department of Mathematics 2001, Pages: 53 In this study, which is prepared as four chapter, we define generalized difference sequence spaces ^«(A"), c(A") and c0(AT), such as for example *.(A-)={x =<*,): (krAmxk)e£"}, where A%= A"-1*, - AmAxk+l, Axk=xk-xk+l, meN={l,2,...} and re 91, and we examine some properties of these sequence spaces. In the first chapter we give the fundamental definitions and theorems. In the second chapter we define the sequence spaces £"(&*), c{Amr) and c0(A"). We show that these sequence spaces are Banach spaces, and also we give the continuous duals of the sequence spaces. In the third chapter we give the a -, fi - and / - duals of these sequence spaces. In the last chapter, we characterize the matrix classes ( X(A"), Y ) where X= lm ore and Y= /. and ( X, Y(A?)) where X= lx or c and Y= *., c or Co. KEY WORDS: Sequence spaces, a -, /?- and y - duals, matrix transformations. II