Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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BOUNDARIES AND PEAK POINTS OF LIPSCHITZ ALGEBRAS

  • MAHYAR, H. (Faculty of Mathematical Sciences and Computer Engineering, University for Teacher Education)
  • Received : 1999.06.28
  • Published : 2000.07.30
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Abstract

We determine the Shilov and Choquet boundaries and the set of peak points of Lipschitz algebras $Lip(X,\;{\alpha})$ for $0<{\alpha}{\leq}1$, and $lip(X,\;{\alpha})$ for $0<{\alpha}<1$, on a compact metric space X. Then, when X is a compact subset of $\mathbb{C}^n$, we define some subalgebras of these Lipschitz algebras and characterize their Shilov and Choquet boundaries. Moreover, for compact plane sets X, we determine the Shilove boundary of them. We also determine the set of peak points of these subalgebras on certain compact subsets X of $\mathbb{C}^n$.

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References

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