Calculations in New Sequence Spaces and Application to Statistical Convergence
In this paper we recall recent results that are direct consequences of the fact that (w∞(λ) ,w∞(λ)) is a Banach algebra. Then we define the set Wτ = Dτw∞ and characterize the sets Wτ (A) where A is either of the operators &am...
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Universidad de La Frontera
2010-01-01
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300008 |
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| author | BRUNO DE MALAFOSSE VLADIMIR RAKOEVIC |
| author_facet | BRUNO DE MALAFOSSE VLADIMIR RAKOEVIC |
| author_sort | BRUNO DE MALAFOSSE |
| collection | DOAJ |
| description | In this paper we recall recent results that are direct consequences of the fact that (w∞(λ) ,w∞(λ)) is a Banach algebra. Then we define the set Wτ = Dτw∞ and characterize the sets Wτ (A) where A is either of the operators Δ, ∑, Δ(λ), or C(λ). Afterwardswe consider the sets [A1,A2]Wτ of all sequences X such that A1 (λ)(|A2(μ) X|) ∈ Wτ where A1 and A2 are of the form C(ξ), C+ (ξ), Δ(ξ), or Δ+ (ξ) and it is given necessary conditions to get |A1 (λ),A2(μ)| Wτ 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/τC(λ)C(μ), D1/τΔ(λ)Δ(μ), D1/τΔ(λ)C(μ). We also give conditions to have xk → 0(S(A)) where A is either of the operators D1/τC+ (λ)Δ(μ), D1/τC(λ)C(μ), D1/τC+ (λ)C+(μ), or D1/τΔ(λ)C+(μ).<br>Recordamos resultados recientes que son consecuencia directa del hecho de que (w∞(λ), w∞(λ)) es una algebra de Banach. Entonces nosotros definimos el conjunto Wτ = Dτw∞y caracterizamos los conjuntos Wτ (A) donde A es uno de los siguientes operadores Δ, ∑, Δ(λ), o C(λ). Después consideramos los conjuntos[A1,A2]Wτ de todas las sucesiones X tal que A1 (λ)(|A2(μ) X|) ∈ Wτ dondeA1 y A2 son de la forma C(ξ), C+ (ξ), Δ(ξ), or Δ+ (ξ) y son dadas condiciones necesarias para obtener |A1 (λ),A2(μ)| Wτ en la forma Wξ. Finalmente, aplicamos los resultados previos para tener xk → L(S(A)) donde A es una de las matrices infinitas D1/τC(λ)C(μ), D1/τΔ(λ)Δ(μ), D1/τΔ(λ)C(μ) . Nosotros también damos condiciones para tener xk → 0(S(A)) donde A es uno de los operadores D1/τC+ (λ)Δ(μ), D1/τC(λ)C(μ), D1/τC+ (λ)C+(μ), o D1/τΔ(λ)C+(μ). |
| first_indexed | 2024-12-19T15:45:29Z |
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| language | English |
| last_indexed | 2024-12-19T15:45:29Z |
| publishDate | 2010-01-01 |
| publisher | Universidad de La Frontera |
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| spelling | doaj.art-6eb728dc4fe6475a81790942aec237902022-12-21T20:15:21ZengUniversidad de La FronteraCubo0716-77760719-06462010-01-01123121138Calculations in New Sequence Spaces and Application to Statistical ConvergenceBRUNO DE MALAFOSSEVLADIMIR RAKOEVICIn this paper we recall recent results that are direct consequences of the fact that (w∞(λ) ,w∞(λ)) is a Banach algebra. Then we define the set Wτ = Dτw∞ and characterize the sets Wτ (A) where A is either of the operators Δ, ∑, Δ(λ), or C(λ). Afterwardswe consider the sets [A1,A2]Wτ of all sequences X such that A1 (λ)(|A2(μ) X|) ∈ Wτ where A1 and A2 are of the form C(ξ), C+ (ξ), Δ(ξ), or Δ+ (ξ) and it is given necessary conditions to get |A1 (λ),A2(μ)| Wτ 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/τC(λ)C(μ), D1/τΔ(λ)Δ(μ), D1/τΔ(λ)C(μ). We also give conditions to have xk → 0(S(A)) where A is either of the operators D1/τC+ (λ)Δ(μ), D1/τC(λ)C(μ), D1/τC+ (λ)C+(μ), or D1/τΔ(λ)C+(μ).<br>Recordamos resultados recientes que son consecuencia directa del hecho de que (w∞(λ), w∞(λ)) es una algebra de Banach. Entonces nosotros definimos el conjunto Wτ = Dτw∞y caracterizamos los conjuntos Wτ (A) donde A es uno de los siguientes operadores Δ, ∑, Δ(λ), o C(λ). Después consideramos los conjuntos[A1,A2]Wτ de todas las sucesiones X tal que A1 (λ)(|A2(μ) X|) ∈ Wτ dondeA1 y A2 son de la forma C(ξ), C+ (ξ), Δ(ξ), or Δ+ (ξ) y son dadas condiciones necesarias para obtener |A1 (λ),A2(μ)| Wτ en la forma Wξ. Finalmente, aplicamos los resultados previos para tener xk → L(S(A)) donde A es una de las matrices infinitas D1/τC(λ)C(μ), D1/τΔ(λ)Δ(μ), D1/τΔ(λ)C(μ) . Nosotros también damos condiciones para tener xk → 0(S(A)) donde A es uno de los operadores D1/τC+ (λ)Δ(μ), D1/τC(λ)C(μ), D1/τC+ (λ)C+(μ), o D1/τΔ(λ)C+(μ).http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300008Banach algebrastatistical convergenceAstatistical convergenceinfinite matrix |
| spellingShingle | BRUNO DE MALAFOSSE VLADIMIR RAKOEVIC Calculations in New Sequence Spaces and Application to Statistical Convergence Cubo Banach algebra statistical convergence Astatistical convergence infinite matrix |
| title | Calculations in New Sequence Spaces and Application to Statistical Convergence |
| title_full | Calculations in New Sequence Spaces and Application to Statistical Convergence |
| title_fullStr | Calculations in New Sequence Spaces and Application to Statistical Convergence |
| title_full_unstemmed | Calculations in New Sequence Spaces and Application to Statistical Convergence |
| title_short | Calculations in New Sequence Spaces and Application to Statistical Convergence |
| title_sort | calculations in new sequence spaces and application to statistical convergence |
| topic | Banach algebra statistical convergence Astatistical convergence infinite matrix |
| url | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300008 |
| work_keys_str_mv | AT brunodemalafosse calculationsinnewsequencespacesandapplicationtostatisticalconvergence AT vladimirrakoevic calculationsinnewsequencespacesandapplicationtostatisticalconvergence |