On Some Sequence Spaces Related to a Sequence in a Normed space

Abstract

In this paper, we introduce some new multiplier sequence spaces by using sequences in a normed space $X$ and matrix domain of Ces\'aro summability method in $\ell_\infty$ and $c_0$. Then we obtain the characterizations of completeness and barrelledness of normed space $X$ through its weakly and weakly* unconditionally Cauchy series.

Keywords

• Mulpilier spaces,weakly unconditionally Cauchy series,completeness,Cesáro sequence spaces,barrelledness

References

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