Open Access

On Some Generalized -Difference Riesz Sequence Spaces and Uniform Opial Property

Journal of Inequalities and Applications20112011:485730

https://doi.org/10.1155/2011/485730

Received: 29 November 2010

Accepted: 18 January 2011

Published: 15 February 2011

Abstract

We define the new generalized difference Riesz sequence spaces , , and which consist of all the sequences whose -transforms are in the Riesz sequence spaces , , and , respectively, introduced by Altay and Başar (2006). We examine some topological properties and compute the -, -, and -duals of the spaces , , and . Finally, we determine the necessary and sufficient conditions on the matrix transformation from the spaces , , and to the spaces and and prove that sequence spaces and have the uniform Opial property for for all .

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Authors’ Affiliations

(1)
Department of Mathematics, Sakarya University, Sakarya, Turkey

Copyright

© M. Başarır and M. Öztürk 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.