On the Riesz Almost Convergent Sequences Space

The purpose of this paper is to introduce new spaces f∧ and f∧0 that consist of all sequences whose Riesz transforms of order one are in the spaces f and f0, respectively. We also show that f∧ and f∧0 are linearly isomorphic to the spaces f and f0, respectively. The β‐ and γ‐duals of the spaces f∧ and f∧0 are computed. Furthermore, the classes (f∧:μ) and (μ:f∧) of infinite matrices are characterized for any given sequence space μ and determine the necessary and sufficient conditions on a matrix A to satisfy BR − core(Ax)⊆K − core(x), BR − core(Ax)⊆st − core(x) for all x ∈ ℓ∞.