Recently several authors defined and studied Riesz sequence space r~q(u, p) of non-absolute type. In this paper for some weight s ≥ 0, we define the generalized Risez sequence space r~q(u, p, s) of non-absolute type and determine its KotheToeplitz dual. We also consider the matrix mapping r~q(u, p, s) to l_∞ and r~q(u, p, s) to c, where l_∞ is the space of all bounded sequences and c is the space of all convergent sequences.
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