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Some paranormed Riesz sequence spaces of non-absolute type. (English) Zbl 1118.46009
Let t=(t k ) be a sequence of positive numbers and T n :=t 0 ++t n (n). For the weighted mean transformation y n :=T n -1 k=0 n t k x k , the authors introduce the Riesz sequence spaces r t (p):={(x k )sup n |y n | p n <}, r 0 t (p):={(x k )lim n |y n | p n =0} and r c t (p):=r 0 t (p) span{(1,1,)} (here p=(p n ) is a bounded sequence with p n >0) and study some of their properties, such as completeness with respect to a paranorm and characterization of the continuous and the Köthe-Toeplitz duals. It is proved that these spaces are linearly isomorphic to the complete paranormed sequence spaces of Maddox, (p), c 0 (p) and c(p), respectively. Some matrix mappings related to the Riesz spaces are characterized.

46A45Sequence spaces
46A35Summability and bases in topological linear spaces