DOMAIN OF CESARO MEAN OF ORDER ONE IN SOME SPACES OF DOUBLE SEQUENCES

In this study, we define the spaces (M) over tilde (u), (C) over tilde (p), (C) over tilde (0p), C-bp, (C) over tilde (r) and (L) over tilde (q) of double sequences whose Cesaro transforms are bounded, convergent in the Pringsheim's sense, null in the Pringsheim's sense, both convergent in the Pringsheim's sense and bounded, regularly convergent and absolutely q-summable, respectively, and also examine some properties of those sequence spaces. Furthermore, we show that these sequence spaces are Banach spaces. We determine the alpha-dual of the space (M) over tilde (u) and the beta(bp)-dual of the space (C) over tilde (r), and beta(v)-dual of the space (C) over tilde (eta) of double sequences, where v, eta is an element of{p, bp, r}. Finally, we characterize the classes ((C) over tilde (bp) : (C) over tilde (v)) and (mu : (C) over tilde (v)) for v is an element of{p, bp, r} of four dimensional matrix transformations, where mu is any given space of double sequences.