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arXiv · 1307.5620

On the spaces of $λ-$ convergent and bounded series

Meltem Kaya·Hasan Furkan
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Abstract

The main purpose of this study is to introduce the spaces $cs^λ, cs_0^λ$ and $bs^λ$ which are $BK-$spaces of non-absolute type. We prove that these spaces are linearly isomorphic to the spaces $cs, cs_0$ and $bs$, respectively and derive some inclusion relations. Additionally, their Schauder bases have been constructed and the $α-,β-$ and $γ-$ duals of these spaces have been computed. Finally, we characterize some matrix classes from the spaces $cs^λ, cs_0^λ$ and $bs^λ$ to spaces $\ell_p, c$ and $c_0$, where $1\leq p\leq\infty$ .

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Meltem Kaya, Hasan Furkan. 2013-07-22. On the spaces of $λ-$ convergent and bounded series. https://arxiv.org/abs/1307.5620

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