충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제24권2호
  • /
  • Pages.337-344
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  • 2011
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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ANOTHER PROOF THAT Aγ(G) AND A∆(G) ARE BANACH ALGEBRAS

  • Lee, Hun Hee (Department of Mathematics, Chungbuk National University)
  • 투고 : 2011.03.29
  • 심사 : 2011.05.24
  • 발행 : 2011.06.30
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초록

We provide another unified proof that $A_{\gamma}(G)$ and $A_{\Delta}(G)$ are Banach algebras for a compact group G, where $A_{\gamma}(G)$ and $A_{\Delta}(G)$ are images of the convolution and the twisted convolution, respectively, on $A(G{\times}G)$. Our new approach heavily depends on analysis of co-multiplication on VN(G), the group von-Neumann algebra of G.

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과제정보

연구 과제 주관 기관 : Chungbuk National University, National Research Foundation of Korea(NRF)

참고문헌

  1. B. E. Forrest, E. Samei and N. Spronk, Convolutions on compact groups and Fourier algebras of coset spaces, Studia Math. 196 (2010), no. 3, 223-249.
  2. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, II. Springer Verlage, 1963.
  3. B. Johnson, Non-amenability of the Fourier algebra of a compact group, J. London Math. Soc. (2) 50 (1994), no. 2, 361-374. https://doi.org/10.1112/jlms/50.2.361