Abstract and Applied Analysis

Domain of the Double Sequential Band Matrix B ( r ~ , s ~ ) in the Sequence Space ( p )

Havva Nergiz and Feyzi Başar

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Abstract

The sequence space ( p ) was introduced by Maddox (1967). Quite recently, the domain of the generalized difference matrix B ( r , s ) in the sequence space p has been investigated by Kirişçi and Başar (2010). In the present paper, the sequence space ( B ~ , p ) of nonabsolute type has been studied which is the domain of the generalized difference matrix B ( r ~ , s ~ ) in the sequence space ( p ) . Furthermore, the alpha-, beta-, and gamma-duals of the space ( B ~ , p ) have been determined, and the Schauder basis has been given. The classes of matrix transformations from the space ( B ~ , p ) to the spaces , c and c0 have been characterized. Additionally, the characterizations of some other matrix transformations from the space ( B ~ , p ) 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

Permanent link to this document
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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