On the Riesz Almost Convergent Sequences Space

Mehmet Şengönül and Kuddusi Kayaduman

Abstract and Applied Analysis, 2012, vol. 2012, 1-18

Abstract:

The purpose of this paper is to introduce new spaces î ð ‘“ and î ð ‘“ 0 that consist of all sequences whose Riesz transforms of order one are in the spaces ð ‘“ and ð ‘“ 0 , respectively. We also show that î ð ‘“ and î ð ‘“ 0 are linearly isomorphic to the spaces ð ‘“ and ð ‘“ 0 , respectively. The ð ›½ - and ð ›¾ - duals of the spaces î ð ‘“ and î ð ‘“ 0 are computed. Furthermore, the classes ( î ð ‘“ ∶ 𠜇 ) and î ( 𠜇 ∶ ð ‘“ ) of infinite matrices are characterized for any given sequence space 𠜇 and determine the necessary and sufficient conditions on a matrix ð ´ to satisfy ð µ ð ‘… − c o r e ( ð ´ ð ‘¥ ) ⊆ ð ¾ âˆ’ c o r e ( ð ‘¥ ) , ð µ ð ‘… − c o r e ( ð ´ ð ‘¥ ) ⊆ ð ‘ ð ‘¡ − c o r e ( ð ‘¥ ) for all ð ‘¥ ∈ â„“ ∞ .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:691694

DOI: 10.1155/2012/691694

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