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Generalization of the sequence space (p) derived by weighted mean. (English) Zbl 1116.46003
Summary: The sequence space (p) was introduced and studied by I. J. Maddox [Q. J. Math., Oxf., II. Ser. 18, 345–355 (1967; Zbl 0156.06602)]. In the present paper, the sequence spaces (u,v;p) of non-absolute type which are derived by the generalized weighted mean are defined and it is proved that the spaces (u,v;p) and (p) are linearly isomorphic. Besides this, the β- and γ-duals of the space (u,v;p) are computed and a basis of that space is constructed. Further, it is established that the sequence space p (u,v) has the AD property and the f-dual of the space p (u,v) is given. Finally, the matrix mappings from the sequence spaces (u,v;p) to the sequence space μ and from the sequence space μ to the sequence space (u,v;p) are characterized.

46A45Sequence spaces