THE SEQUENCE SPACE $\mathcal C(p)$ AND RELATED MATRIX TRANSFORMATIONS
DOI:
https://doi.org/10.5556/j.tkjm.21.1990.4668Keywords:
Sequence space, Matrix transformations, Incomplete space, Kothe- Toeplitz dualAbstract
In this paper we define the sequence space $\mathcal C(p)$ defined in an incomplete seminormed space $(X,g)$, namely
\[ \mathcal C(p) = \{(x_k) \subset X: \sup_{r\ge 1}g(x_k - x_{k+r})^{p_k}\to 0, k\to\infty \} \]
where $p =(p_k)$ is a sequence of positive numbers. Then we investigated some of its fundamental properties and some of related matrix transformations.
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