## Annals of Functional Analysis

### On Some Difference Sequence Spaces of Weighted Means and Compact Operators‎

#### Abstract

‎In the peresent paper‎, ‎by using generalized weighted mean and difference‎ ‎matrix of order $m,$ we introduce the sequence spaces $X(u,v,\Delta^{(m)})$‎, ‎where $X$ is one of the spaces $\ell_{\infty}$‎, ‎$c$ or $c_{0}$‎. ‎Also‎, ‎we‎ ‎determine the $\alpha$-‎, ‎$\beta$‎- ‎and $\gamma$-duals of those spaces and‎ ‎construct their Schauder bases for $X\in\{c,c_{0}\}$‎. ‎Morever‎, ‎we give the‎ ‎characterization of the matrix mappings on the spaces $X(u,v,\Delta^{m})$‎ ‎ for $X\in\{\ell_{\infty},c,c_{0}\}.$ Finally‎, ‎we characterize some‎ ‎classes of compact operators on the spaces $\ell_{\infty}(u,v,\Delta^{m})$ and‎ ‎$c_{0}(u,v,\Delta^{m})$ by using the Hausdorff measure of noncompactness‎.

#### Article information

Source
Ann. Funct. Anal., Volume 2, Number 2 (2011), 114-129 .

Dates
First available in Project Euclid: 12 May 2014

https://projecteuclid.org/euclid.afa/1399900200

Digital Object Identifier
doi:10.15352/afa/1399900200

Mathematical Reviews number (MathSciNet)
MR2855292

Zentralblatt MATH identifier
1259.46003

Subjects
Secondary: 46B15‎ ‎46B50

#### Citation

Başarır, Metin; Kara, Emrah Evren. On Some Difference Sequence Spaces of Weighted Means and Compact Operators‎. Ann. Funct. Anal. 2 (2011), no. 2, 114--129. doi:10.15352/afa/1399900200. https://projecteuclid.org/euclid.afa/1399900200

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