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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 \(\widetilde c_0\) and \(\widetilde c\) of nonabsolute type which are BK-spaces including the spaces \(c_0\) and \(c\) are introduced and it is proved that the spaces \(\widetilde c_0\) and \(\widetilde c\) are linearly isomorphic to the spaces \(c_0\) and \(c\), respectively. Additionally, the \(\alpha\)-, \(\beta\)- and \(\gamma\)-duals of the spaces \(\widetilde c_0\) and \(\widetilde c\) are computed and their bases are constructed. Finally, matrix mappings from the space \(\widetilde c\) to \(\mu\) and from the space \(\mu\) to \(\widetilde c\) are characterized by employing the suitable relations between the corresponding matrix classes, where \(\mu\) is any given sequence space.

46A45 Sequence spaces (including Köthe sequence spaces)
46B45 Banach sequence spaces
46A35 Summability and bases in topological vector spaces