The continuity of superposition operators on some sequence spaces defined by moduli |
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Authors: | Enno Kolk Annemai Raidjõe |
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Institution: | (1) Institute of Pure Mathematics, University of Tartu, 50090 Tartu, Estonia;(2) Institute of Mathematics, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, Estonia |
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Abstract: | Let λ and μ be solid sequence spaces. For a sequence of modulus functions Φ = (ϕ k) let λ(Φ) = {x = (x
k
): (ϕk(|x
k
|)) ∈ λ}. Given another sequence of modulus functions Ψ = (ψk), we characterize the continuity of the superposition operators P
f
from λ(Φ) into μ (Ψ) for some Banach sequence spaces λ and μ under the assumptions that the moduli ϕk (k ∈ ℕ) are unbounded and the topologies on the sequence spaces λ(Φ) and μ(Ψ) are given by certain F-norms. As applications
we consider superposition operators on some multiplier sequence spaces of Maddox type.
This research was supported by Estonian Science Foundation Grant 5376. |
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Keywords: | sequence space superposition operator modulus function continuity |
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