On the Riesz Almost Convergent Sequences Space

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„“ ∞ .