On the m^th order difference sequence space of generalized weighted mean and compact operators

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• 作者：Metin BA?ARIR^a ; ^{basarir@sakarya.edu.tr} ; Emrah Evren KARA^b ; ^{emrah.kara@bilecik.edu.tr}
• 关键词：Paranormed sequence spaces ; difference sequence spaces ; weighted mean ; ¦Á-¦Â- ; ¦Ã-duals ; matrix mappings ; Hausdorff measure of noncompactness ; compact operators
• 刊名：Acta Mathematica Scientia
• 出版年：2013
• 出版时间：May, 2013
• 年：2013
• 卷：33
• 期：3
• 页码：797-813
• 全文大小：367 K

文摘

In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space ?(u, v, p; ¦¤^(m)), which consist of the sequences whose generalized weighted ¦¤^(m)-difference means are in the linear space ?(p) defined by I.J. Maddox. Also, we determine the basis of this space and compute its ¦Á-, ¦Â- and ¦Ã-duals. Further, we give the characterization of the classes of matrix mappings from ?(u, v, p, ¦¤^(m)) to ?_¡Þ, c and c₀. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space ?_p(u, v, ¦¤^(m))(1 ¡Ü p < ¡Þ).