Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON MULTIPLIER WEIGHTED-SPACE OF SEQUENCES

  • Received : 2020.02.06
  • Accepted : 2020.07.02
  • Published : 2020.10.31
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Abstract

We consider the weighted spaces ℓp(𝕊, 𝜑) and ℓp(𝕊, 𝜓) for 1 < p < +∞, where 𝜑 and 𝜓 are weights on 𝕊 (= ℕ or ℤ). We obtain a sufficient condition for ℓp(𝕊, 𝜓) to be multiplier weighted-space of ℓp(𝕊, 𝜑) and ℓp(𝕊, 𝜓). Our condition characterizes the last multiplier weighted-space in the case where 𝕊 = ℤ. As a consequence, in the particular case where 𝜓 = 𝜑, the weighted space ℓp(ℤ,𝜓) is a convolutive algebra.

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Acknowledgement

The authors would like to thank the referees for their helpful remarks and valuables corrections.

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