Abstract and Applied Analysis

Generalized Difference Spaces of Non-Absolute Type of Convergent and Null Sequences

Abstract

The aim of the present paper is to introduce the spaces ${c}_{0}^{\lambda }(B)$ and ${c}^{\lambda }(B)$ of generalized difference sequences which generalize the paper due to Mursaleen and Noman (2010). These spaces are the BK-spaces of non-absolute type and norm isomorphic to the spaces ${c}_{0}$ and $c$, respectively. Furthermore, we derive some inclusion relations determine the $\alpha \text{-}$, $\beta \text{-}$, and $\gamma \text{-}$duals of those spaces, and construct their Schauder bases. Finally, we characterize some matrix classes from the spaces ${c}_{0}^{\lambda }(B)$, and ${c}^{\lambda }(B)$ to the spaces ${\ell }_{p}$, ${c}_{0}$, and c.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 435076, 20 pages.

Dates
First available in Project Euclid: 28 March 2013

https://projecteuclid.org/euclid.aaa/1364475918

Digital Object Identifier
doi:10.1155/2012/435076

Mathematical Reviews number (MathSciNet)
MR2994943

Zentralblatt MATH identifier
1267.46017

Citation

Sönmez, Abdulcabbar; Başar, Feyzi. Generalized Difference Spaces of Non-Absolute Type of Convergent and Null Sequences. Abstr. Appl. Anal. 2012 (2012), Article ID 435076, 20 pages. doi:10.1155/2012/435076. https://projecteuclid.org/euclid.aaa/1364475918

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