International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 1, Article ID 46930, 5 pages
doi:10.1155/IJMMS/2006/46930
Measure of noncompactness of operators and matrices on the spaces c and c0
Bruno De Malafosse1
, Eberhard Malkowsky2
and Vladimir Rakočević3
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 Ni {s}, Vi {s}egradska 33, Ni {s} 18000, Serbia and Montenegro
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.