On the Riesz Almost Convergent Sequences Space

Mehmet Şengönül and Kuddusi Kayaduman

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: 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∞.

Date: 2012
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https://doi.org/10.1155/2012/691694

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:691694

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