Hausdorff measure of noncompactness in some sequence spaces of a triple band matrix. (English) Zbl 1319.47031

Summary: The sequence spaces \(c_0 (B)\), \(\ell_\infty(B)\) have recently been introduced by A. Sönmez [Comput. Math. Appl. 62, No. 2, 641–650 (2011; Zbl 1228.40006)]. In this paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the spaces \(c_0 (B)\), \(\ell_\infty(B)\) and, by using the Hausdorff measure of noncompactness, we characterize some classes of compact operators on these spaces.


47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
46A45 Sequence spaces (including Köthe sequence spaces)
40H05 Functional analytic methods in summability
40C05 Matrix methods for summability


Zbl 1228.40006
Full Text: DOI


[1] doi:10.1016/j.camwa.2011.05.045 · Zbl 1228.40006 · doi:10.1016/j.camwa.2011.05.045
[2] doi:10.1016/j.camwa.2010.06.005 · Zbl 1201.40002 · doi:10.1016/j.camwa.2010.06.005
[3] doi:10.1016/j.laa.2011.06.014 · Zbl 1231.47029 · doi:10.1016/j.laa.2011.06.014
[4] doi:10.1016/j.amc.2006.12.024 · Zbl 1132.46011 · doi:10.1016/j.amc.2006.12.024
[5] doi:10.1016/j.jmaa.2007.08.021 · Zbl 1147.47002 · doi:10.1016/j.jmaa.2007.08.021
[6] doi:10.1016/j.jmaa.2011.01.028 · Zbl 1236.46015 · doi:10.1016/j.jmaa.2011.01.028
[7] doi:10.1016/j.jmaa.2012.02.031 · Zbl 1248.46005 · doi:10.1016/j.jmaa.2012.02.031
[8] doi:10.1016/S0096-3003(02)00674-4 · Zbl 1035.46001 · doi:10.1016/S0096-3003(02)00674-4
[9] doi:10.1016/j.amc.2007.09.008 · Zbl 1148.46007 · doi:10.1016/j.amc.2007.09.008
[10] doi:10.1016/j.na.2010.06.030 · Zbl 1211.47061 · doi:10.1016/j.na.2010.06.030
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