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Journal of Function Spaces
Volume 2014, Article ID 196489, 7 pages
http://dx.doi.org/10.1155/2014/196489
Research Article

Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces

1Department of Mathematics, University of Giessen, Arndtstraβe 2, 35392 Giessen, Germany
2Department of Mathematics, Faculty of Arts and Sciences, Fatih University, Büyükçekmece, 34500 Istanbul, Turkey
3Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 20 May 2013; Accepted 31 October 2013; Published 10 February 2014

Academic Editor: Adrian Petrusel

Copyright © 2014 E. Malkowsky and A. Alotaibi. 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 study the spaces , , and of sequences that are strongly summable to 0, summable, and bounded with index by the Cesàro method of order 1 and establish the representations of the general bounded linear operators from the spaces into the spaces , , and . We also give estimates for the operator norm and the Hausdorff measure of noncompactness of such operators. Finally we apply our results to characterize the classes of compact bounded linear operators from and into and .