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On some new sequence spaces of non-absolute type related to the spaces p and II. (English) Zbl 1276.46004

The spaces p λ and λ of non-absolute type were introduced by the same authors in Part I [Filomat 25, No. 2, 33–51 (2011; Zbl 1265.46011)] as the spaces of all sequences whose Λ-transforms are in the spaces p and , respectively, where 1p<. The present paper is a natural continuation of the work done in that paper.

The paper is divided mainly in two parts in connection with new results besides the introduction, a general description of the spaces p λ and λ , and references. In the first part, the α-, β-, γ-duals of the spaces p λ and λ are computed. In the second part, the matrix classes ( p λ : ), ( p λ :c), ( p λ :c 0 ), ( p λ : 1 ), ( 1 λ : p ) and ( λ : p ), where 1p<, are characterized. Further, the authors deduce a characterization of some other classes by means of a given basic lemma.

MSC:
46A45Sequence spaces
40C05Matrix methods in summability
40H05Functional analytic methods in summability