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On New Classes of Sequence Spaces Inclusion Equations Involving the Sets C0, C, lP, (1 ≤ P ≤ ∞), W0 and W∞


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1 Universite du Havre, France
     

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Given any sequence a = (an)n≥1 of positive real numbers and any set E of complex sequences, we write Ea for the set of all sequences y = (yn)n≥1 such that y/a = (yn/an)n≥1 ∈ E; in particular, ca denotes the set of all sequences y such that y/a converges. Let Φ = {c0, c, l∞, lp, w0, w∞},(p≥1).. In this paper we apply a result stated in [9] and we deal with the class of (SSIE) of the form F ⊂ Ea+F'x where F∈{c0,lp, w0, w∞} and E, F' ∈ Φ. We then obtain the solvability of the corresponding (SSIE) in the particular case when a = (rn)n and we deal with the case when F = F'. Finally we solve the equation Er + (lp)x = lp with E = c0, c, s1, or lp (p≥1). These results extend those stated in [10].


Keywords

BK Space, Matrix Transformations, Multiplier of Sequence Spaces, Sequence Spaces Inclusion Equations, Sequence Spaces Inclusion Equations with Operator.
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  • On New Classes of Sequence Spaces Inclusion Equations Involving the Sets C0, C, lP, (1 ≤ P ≤ ∞), W0 and W∞

Abstract Views: 292  |  PDF Views: 2

Authors

Bruno de Malafosse
Universite du Havre, France

Abstract


Given any sequence a = (an)n≥1 of positive real numbers and any set E of complex sequences, we write Ea for the set of all sequences y = (yn)n≥1 such that y/a = (yn/an)n≥1 ∈ E; in particular, ca denotes the set of all sequences y such that y/a converges. Let Φ = {c0, c, l∞, lp, w0, w∞},(p≥1).. In this paper we apply a result stated in [9] and we deal with the class of (SSIE) of the form F ⊂ Ea+F'x where F∈{c0,lp, w0, w∞} and E, F' ∈ Φ. We then obtain the solvability of the corresponding (SSIE) in the particular case when a = (rn)n and we deal with the case when F = F'. Finally we solve the equation Er + (lp)x = lp with E = c0, c, s1, or lp (p≥1). These results extend those stated in [10].


Keywords


BK Space, Matrix Transformations, Multiplier of Sequence Spaces, Sequence Spaces Inclusion Equations, Sequence Spaces Inclusion Equations with Operator.

References