Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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(σ, σ)-DERIVATION AND (σ, 𝜏)-WEAK AMENABILITY OF BEURLING ALGEBRA

  • Chen, Lin (College of Mathematics and Information Science Shaanxi Normal University, Department of Mathematics and Physics Anshun University) ;
  • Zhang, Jianhua (College of Mathematics and Information Science Shaanxi Normal University)
  • Received : 2020.10.14
  • Accepted : 2020.12.30
  • Published : 2021.09.30
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Abstract

Let G be a topological group with a locally compact and Hausdorff topology. Let ω be a diagonally bounded weight on G. In this paper, (σ, σ)-derivation and (σ, 𝜏)-weak amenability of the Beurling algebra L1ω(G) are studied, where σ, 𝜏 are isometric automorphisms of L1ω(G). We prove that every continuous (σ, σ)-derivation from L1ω(G) into measure algebra Mω(G) is (σ, σ)-inner and the Beurling algebra L1ω(G) is (σ, 𝜏)-weakly amenable.

Keywords

Acknowledgement

This work is supported by the National Natural Science Foundation of China (No. 12061018) and the Postdoctoral Science Foundation of China (No. 2018M633450). The first author is supported by Foundation of Educational Commission (No. KY[2017]092) and of Science and Technology department (No. [2018]1001) of Guizhou Province of China.

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