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PROJECTIVE LIMIT OF A SEQUENCE OF BANACH FUNCTION ALGEBRAS AS A FRECHET FUNCTION ALGEBRA
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 Title & Authors
PROJECTIVE LIMIT OF A SEQUENCE OF BANACH FUNCTION ALGEBRAS AS A FRECHET FUNCTION ALGEBRA
Sady. F.;
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 Abstract
Let X be a hemicompact space with () as an admissible exhaustion, and for each n N, a Banach function algebra on with respect to such that and for all f, We consider the subalgebra A = { f C(X) : of C(X) as a frechet function algebra and give a result related to its spectrum when each 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;
 Language
English
 Cited by
1.
Separating maps on Fréchet algebras, Quaestiones Mathematicae, 2014, 37, 1, 67  crossref(new windwow)
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T. G. Honary and H. Mahyar, Approximation in Lipschitz algebras of infinitely differentiable functions, Bull. Korean Math. Soc. 36 (1999), 629-636.

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F. Sady, Relations between Banach function algebras and Fréchet function algebras, Honam Math. J. 20 (1998), 79-88.

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D. R. Sherbert, The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc. 111 (1964), 240-272. crossref(new window)