대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제52권4호
  • /
  • Pages.1123-1132
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  • 2015
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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DERIVATIONS ON CONVOLUTION ALGEBRAS

  • 투고 : 2014.04.08
  • 발행 : 2015.07.31
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초록

In this paper, we investigate derivations on the noncommutative Banach algebra $L^{\infty}_0({\omega})^*$ equipped with an Arens product. As a main result, we prove the Singer-Wermer conjecture for the noncommutative Banach algebra $L^{\infty}_0({\omega})^*$. We then show that a derivation on $L^{\infty}_0({\omega})^*$ is continuous if and only if its restriction to rad($L^{\infty}_0({\omega})^*$) is continuous. We also prove that there is no nonzero centralizing derivation on $L^{\infty}_0({\omega})^*$. Finally, we prove that the space of all inner derivations of $L^{\infty}_0({\omega})^*$ is continuously homomorphic to the space $L^{\infty}_0({\omega})^*/L^1({\omega})$.

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참고문헌

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피인용 문헌

  1. Generalized derivations on some convolution algebras vol.92, pp.2, 2018, https://doi.org/10.1007/s00010-017-0531-6