# Some base spaces and core theorems of new type

Volume 9, Issue 2, pp 377--391 Publication Date: February 21, 2016
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### Authors

Zarife Zararsiz - Science and Art Faculty, Nevşehir Hacı Bektaş Veli University, 50300, Nevşehir, Turkey. Mehmet Şengönül - Science and Art Faculty, Nevşehir Hacı Bektaş Veli University, 50300, Nevşehir, Turkey. Kuddusi Kayaduman - Science and Art Faculty, G. Antep University, 27000, G. Antep, Turkey.

### Abstract

In this paper, we constructed two new base sequence spaces, denoted $rf$ and $rf_0$, and we investigated some of their important properties. Then, by using matrix domains, we defined other sequence spaces on these base spaces, called $zrf$ and $zrf_0$. Finally, we introduced the $B_\hat{R}$ core of a complex-valued sequence and we examined some inclusion theorems related to this new type of core.

### Keywords

• Almost convergence
• base space
• isomorphism
• dual
• matrix transformation
• core theorem

•  40C05
•  46A45
•  40J05

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