Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces. (10th February 2014)

• Record Type: Journal Article
• Authors: Malkowsky, E.; Alotaibi, A.
• Other Names: Petrusel Adrian Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-02-10
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/196489
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We study the spacesw 0 p, w p, andw ∞ p of sequences that are strongly summable to 0, summable, and bounded with indexp ≥ 1 by the Cesàro method of order 1 and establish the representations of the general bounded linear operators from the spacesw p into the spacesw ∞ 1, w 1, andw 0 1 . 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 fromw 0 p andw p intow 0 1 andw 1 .