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Some new Cesàro sequence spaces of non-absolute type which include the spaces c 0 and c. (English) Zbl 1085.46500
Summary: In the present paper, the Cesàro sequence spaces c ˜ 0 and c ˜ of nonabsolute type which are BK-spaces including the spaces c 0 and c are introduced and it is proved that the spaces c ˜ 0 and c ˜ are linearly isomorphic to the spaces c 0 and c, respectively. Additionally, the α-, β- and γ-duals of the spaces c ˜ 0 and c ˜ are computed and their bases are constructed. Finally, matrix mappings from the space c ˜ to μ and from the space μ to c ˜ are characterized by employing the suitable relations between the corresponding matrix classes, where μ is any given sequence space.
MSC:
46A45Sequence spaces
46B45Banach sequence spaces
46A35Summability and bases in topological linear spaces