The lacunary strong Zweier convergent sequence spaces
Commun. Korean Math. Soc. 2010 Vol. 25, No. 1, 51-57
https://doi.org/10.4134/CKMS.2010.25.1.51
Printed March 1, 2010
Mehmet Seng\"on\"ul
Nev\c{s}ehir University
Abstract : In this paper we introduce and study the lacunary strong Zweier sequence spaces $N_{\theta}^0[\mathcal{Z}],~~N_{\theta}[\mathcal{Z}]$ consisting of all sequences $x=(x_k)$ such that $(Zx)$ in the space $N_{\theta}$ and $N_{\theta}^0$ respectively, which is normed. Also, prove that $N_{\theta}^0[\mathcal{Z}],~~N_{\theta}[\mathcal{Z}]$ are linearly isomorphic to the space $N_{\theta}^0$ and $N_{\theta}$, respectively. And we study some connections between lacunary strong Zweier sequence and lacunary statistical Zweier convergence sequence.
Keywords : lacunary sequence, Zweier space, statisticial convergence, Banach space, isomorphism
MSC numbers : Primary 40C05, 40J05, 46A45
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