A new sequence space isomorphic to the space ℓ(p) and compact operators

Murat Candan

Abstract


As a major issue in this work, we present the paranormed sequence space ℓ(u,v,p;B) consisting of all sequences whose R-transforms are in the linear space ℓ(p) introduced by Maddox [Quart. J. Math. Oxford (2), 18(1967), 345--355], where B=B(r,s) denotes double sequential band matrix provided that (r_{n})_{n=0}^{∞} and (s_{n})_{n=0}^{∞} are given convergent sequences of positive real numbers. For this purpose, we have used the generalized weighted mean G and double sequential band matrix B. Meanwhile, we have also presented the basis of this space and computed its α-, β- and γ-duals. Then, we have characterized the classes of matrix mappings from ℓ(u,v,p;B) to ℓ_{∞}, c and c₀. In conclusion, in order to characterize some classes of compact operators given by matrices on the space ℓ_{p}(u,v,B)  (1≤p<∞), we have applied the Hausdorff measure of noncompactness.

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How to Cite this Article:

Murat Candan, A new sequence space isomorphic to the space ℓ(p) and compact operators, Journal of Mathematical and Computational Science, Vol 4, No 2 (2014), 306-334

Copyright © 2014 Murat Candan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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