Calculations in new sequence spaces and application to statistical convergence
- Bruno De Malafosse bdemalaf@wanadoo.fr
- Vladimir RakoÄević vrakoc@bankerinter.net
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DOI:
https://doi.org/10.4067/S0719-06462010000300008Abstract
In this paper we recall recent results that are direct consequences of the fact that (ω∞ (λ),ω∞ (λ)) is a Banach algebra. Then we define the set WÏ„ = Dτω∞ and characterize the sets WÏ„ (A) where A is either of the operators ∆, Σ, ∆(λ), or C(λ). Afterwards we consider the sets [A1, A2]WÏ„ of all sequences X such that A1 (λ) (Ç€A2(µ)XÇ€) ∈ WÏ„ where A1 and A2 are of the form C(ξ), C+ (ξ), ∆(ξ), or ∆+ (ξ) and it is given necessary conditions to get [A1 (λ), A2 (µ)]WÏ„ in the form Wξ. Finally we apply the previous results to statistical convergence. So we have conditions to have xk → L(S(A)) where A is either of the infinite matrices D1/Ï„C(λ)C(µ), D1/τ∆(λ)∆(µ), D1/τ∆(λ)C(µ). We also give conditions to have xk → 0(S(A)) where A is either of the operators D1/Ï„C+ (λ)∆(µ), D1/Ï„C+ (λ)C(µ), D1/Ï„C+(λ)C+(µ), or D1/τ∆(λ)C+(µ).