## Abstract and Applied Analysis

### Domain of the Double Sequential Band Matrix $B\left(\stackrel{~}{r},\stackrel{~}{s}\right)$ in the Sequence Space $\ell {\left(p\right)}^{\ast }$

#### Abstract

The sequence space $\ell \left(p\right)$ was introduced by Maddox (1967). Quite recently, the domain of the generalized difference matrix $B\left(r,s\right)$ in the sequence space ${\ell }_{p}$ has been investigated by Kirişçi and Başar (2010). In the present paper, the sequence space $\ell \left(\stackrel{~}{B},p\right)$ of nonabsolute type has been studied which is the domain of the generalized difference matrix $B\left(\stackrel{~}{r},\stackrel{~}{s}\right)$ in the sequence space $\ell \left(p\right)$. Furthermore, the alpha-, beta-, and gamma-duals of the space $\ell \left(\stackrel{~}{B},p\right)$ have been determined, and the Schauder basis has been given. The classes of matrix transformations from the space $\ell \left(\stackrel{~}{B},p\right)$ to the spaces ${\ell }_{\infty }$, c and c0 have been characterized. Additionally, the characterizations of some other matrix transformations from the space $\ell \left(\stackrel{~}{B},p\right)$ to the Euler, Riesz, difference, and so forth sequence spaces have been obtained by means of a given lemma. The last section of the paper has been devoted to conclusion.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 949282, 10 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511853

Digital Object Identifier
doi:10.1155/2013/949282

Mathematical Reviews number (MathSciNet)
MR3045057

Zentralblatt MATH identifier
1282.46010

#### Citation

Nergiz, Havva; Başar, Feyzi. Domain of the Double Sequential Band Matrix $B\left(\stackrel{~}{r},\stackrel{~}{s}\right)$ in the Sequence Space $\ell {\left(p\right)}^{\ast }$. Abstr. Appl. Anal. 2013 (2013), Article ID 949282, 10 pages. doi:10.1155/2013/949282. https://projecteuclid.org/euclid.aaa/1393511853

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