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Abstract and Applied Analysis
Volume 2013, Article ID 817659, 6 pages
Research Article

The Hahn Sequence Space Defined by the Cesáro Mean

Department of Mathematical Education, Hasan Ali Yücel Education Faculty, Istanbul University, Vefa, Fatih, 34470 Istanbul, Turkey

Received 11 April 2013; Revised 4 July 2013; Accepted 1 August 2013

Academic Editor: Feyzi Başar

Copyright © 2013 Murat Kirişci. 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.


The -space of all sequences is given as such that converges and is a null sequence which is called the Hahn sequence space and is denoted by . Hahn (1922) defined the space and gave some general properties. G. Goes and S. Goes (1970) studied the functional analytic properties of this space. The study of Hahn sequence space was initiated by Chandrasekhara Rao (1990) with certain specific purpose in the Banach space theory. In this paper, the matrix domain of the Hahn sequence space determined by the Cesáro mean first order, denoted by , is obtained, and some inclusion relations and some topological properties of this space are investigated. Also dual spaces of this space are computed and, matrix transformations are characterized.