On the Riesz Almost Convergent Sequences Space

Abstract EN

The purpose of this paper is to introduce new spaces f̂ and f̂0 that consist of all sequences whose Riesz transforms of order one are in the spaces f and f0, respectively.

We also show that f̂ and f̂0 are linearly isomorphic to the spaces f and f0, respectively.

The β- and γ-duals of the spaces f̂ and f̂0 are computed.

Furthermore, the classes (f̂:μ) and (μ:f̂) 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∞.