대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권2호
  • /
  • Pages.451-459
  • /
  • 2023
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A CHARACTERIZATION OF ZERO DIVISORS AND TOPOLOGICAL DIVISORS OF ZERO IN C[a, b] AND ℓ∞

  • 투고 : 2022.04.22
  • 심사 : 2022.12.22
  • 발행 : 2023.04.30
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초록

We give a characterization of zero divisors of the ring C[a, b]. Using the Weierstrass approximation theorem, we completely characterize topological divisors of zero of the Banach algebra C[a, b]. We also characterize the zero divisors and topological divisors of zero in ℓ∞. Further, we show that zero is the only zero divisor in the disk algebra 𝒜 (𝔻) and that the class of singular elements in 𝒜 (𝔻) properly contains the class of topological divisors of zero. Lastly, we construct a class of topological divisors of zero of 𝒜 (𝔻) which are not zero divisors.

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참고문헌

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