\(C_{\lambda}\)-semiconservative FK-spaces
By the definition given by \textit{A. K. Snyder} and \textit{A. Wilansky} [Rocky Mt. J. Math. 2, No. 4, 595--603 (1972; Zbl 0267.40002)], an FK-space \(X\) containing the unit sequences \(\delta^{k}=\left( \delta_{ki}\right) _{i\in\mathbb{N}}\) \(\left( k\in\mathbb{N}\right) \) is called semiconservative if the series \(\sum_{k}f\left( \delta^{k}\right) \) is convergent for each \(f\in X^{\prime}\). If this series is \(A\)-summable, then we speak of the \(A\)-semiconservativity of \(X\). \textit{H. G. Ince} [Math. Commun. 14, No. 1, 157--165 (2009; Zbl 1184.40006)] considered the case \(A=C\), the Cesàro method. In the paper under review, the author studies \(C_{\lambda}\)-semiconservative FK-spaces, where \(C_{\lambda}\) is the submethod of \(C\) defined by the transformation \(y_{n}=\frac{1}{\lambda_{n}}\sum _{k=1}^{\lambda_{n}}\sum_{i=1}^{k}x_{i}\) \ \(\left( n\in\mathbb{N}\right) \) for an index sequence \(\lambda=\left( \lambda_{n}\right) \).
scientific article; zbMATH DE number 6133799
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