On the Riesz Almost Convergent Sequences Space

Abstract

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