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Almost Sequence Spaces Derived by the Domain of the Matrix Ar

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  • Ali Karaisa
  • Ümıt Karabıyık

Abstract

By using Ar, we introduce the sequence spaces afr, af0r, and afsr of normed space and BK‐space and prove that afr, af0r, and afsr are linearly isomorphic to the sequence spaces f, f0, and fs , respectively. Further, we give some inclusion relations concerning the spaces afr, af0r, and the nonexistence of Schauder basis of the spaces fs and afsr is shown. Finally, we determine the β‐ and γ‐duals of the spaces afr and afsr. Furthermore, the characterization of certain matrix classes on new almost convergent sequence and series spaces has exhaustively been examined.

Suggested Citation

Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:783731
DOI: 10.1155/2013/783731
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