Abstract and Applied Analysis
Volume 2012 (2012), Article ID 378250, 10 pages
http://dx.doi.org/10.1155/2012/378250
Research Article

Applications of Measure of Noncompactness in Matrix Operators on Some Sequence Spaces

M. Mursaleen1,2 and A. Latif3

1Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2Department of Mathematics, Tabuk University, Tabuk, Saudi Arabia
3Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 10 November 2011; Accepted 3 January 2012

Academic Editor: Paul Eloe

Copyright © 2012 M. Mursaleen and A. Latif. 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.

Abstract

We determine the conditions for some matrix transformations from 𝑛 ( 𝜙 ) , where the sequence space 𝑛 ( 𝜙 ) , which is related to the ℓ 𝑝 spaces, was introduced by Sargent (1960). We also obtain estimates for the norms of the bounded linear operators defined by these matrix transformations and find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness.