Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 391, Issue 1, Pages 67-81Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2012.02.031
Keywords
Paranormed sequence spaces; B-difference sequence spaces; Weighted mean; alpha-, beta-, gamma-duals; Matrix mappings; Hausdorff measure of noncompactness; Compact operators
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In the present paper, by using generalized weighted mean and difference matrix B, we introduce the paranormed sequence space l(u, v, p; B) which consist of all sequences whose generalized weighted B-difference means are in the linear space l(p) introduced by I.J. Maddox. Also, we give the basis of this space and compute its alpha-, beta- and gamma-duals. Further, we characterize the classes of matrix mappings from l(u, v, p; B) to l(infinity), c and c(0). Finally, we apply the Hausdorff measure of noncompactness to characterize some classes of compact operators given by matrices on the space lp(u, v; B) (1 <= p < infinity). (c) 2012 Elsevier Inc. All rights reserved.
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