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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.

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