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PROJECTIVE LIMIT OF A SEQUENCE OF BANACH FUNCTION ALGEBRAS AS A FRECHET FUNCTION ALGEBRA

  • Sady. F.
  • Published : 2002.05.01

Abstract

Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.

Keywords

Frechet Lipschitz algegra;admissible exhaustion;Lipschitz algebra;Frechet algebra

References

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Cited by

  1. Separating maps on Fréchet algebras vol.37, pp.1, 2014, https://doi.org/10.2989/16073606.2013.779603