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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 46930, 5 pages
http://dx.doi.org/10.1155/IJMMS/2006/46930

Measure of noncompactness of operators and matrices on the spaces c and c0

1LMAH Université du Havre, IUT du Havre, BP 4006, Le Havre 76610, France
2Mathematisches Institut, Universität Giessen, Arndtstrasse 6, Giessen D-35392, Germany
3Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš 18000, Serbia and Montenegro

Received 16 September 2005; Revised 11 December 2005; Accepted 4 January 2006

Copyright © 2006 Hindawi Publishing Corporation. 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

In this note, using the Hausdorff measure of noncompactness, necessary and sufficient conditions are formulated for a linear operator and matrices between the spaces c and c0 to be compact. Among other things, some results of Cohen and Dunford are recovered.