Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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PRIME IDEALS IN LIPSCHITZ ALGEBRAS OF FINITE DIFFERENTIABLE FUNCTIONS

  • EBADIAN, ALI (Faculty of Mathematical Sciences and Computer Engineering, University for Teacher Education)
  • Received : 1999.11.27
  • Published : 2000.07.30
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Abstract

Lipschitz Algebras Lip(X, ${\alpha}$) and lip(X, ${\alpha}$) were first studied by D. R. Sherbert in 1964. B. Pavlovic in 1995 shown that in these algebras, the prime ideals containing a given prime ideal form a chain. In this paper, we show that the above property holds in $Lip^n(X,\;{\alpha})$ and $lip^n(X,\;{\alpha})$, the Lipschitz algebras of finite differentiable functions on a perfect compact place set X.

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References

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  2. Bull. KMS Approximation in Lipschitz algebras of Infinitely Differentiable Functions Honary, T.G.;Mahyar, H.
  3. J. Funct. Anal. v.131 no.1 Automatic Continuity of Lipschitz Algebras Paulovic, Branka
  4. Trans. Amer. Math. Soc. The structure of ideals and point derivations in Banach algebra of Lipschitz functionsjour Sherbert, D.R.