Measure of Noncompactness of Matrix Operators on Some New Difference Sequence Spaces of Order m^th

Kızmaz [13] studied the difference sequence spaces ℓ∞(∆), c(∆) and c0(∆).Several papers dealt with the sets of sequences the mth order difference ofwhich are bounded, convergent or convergent to zero. Aydın and Ba¸sar [6]introduced the sequence spaces a^r0 and a^rc. The main purpose of the presentpaper is to introduce the spaces a^r0(∆^(m)) and arc(∆^(m)) consisting of all sequenceswhose mth order differences are in the spaces ar0 and arc, respectively.Furthermore, the basis for the difference spaces a^r0(∆^(m)) and a^rc(∆^(m)), andthe α−, β− and γ−duals of the difference spaces a^r0(∆^(m)) and a^rc(∆^(m))have been determined. Moreover, the matrix classes (a^rc(∆^(m)) : ℓp) and(a^rc(∆^(m)) : c) have been characterized. Finally, we have characterized thesubclasses K(a^rc(∆^(m)), Y ) of compact operators by applying the Hausdorffmeasure of noncompactness; where Y is one of the spaces c0, c, ℓ1, ℓ1, bv andc(∆)