The Maximal Ideal Space of Extended Di erentiable Lipschitz Algebras
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X, K) is natural.
Abstract
In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X, K) is natural.
참고문헌 (10)
- M. Abtahi, "Normed algebras of infinitely differentiable Lipschitz functions", Quaest. Math, 35(2), pp.195~202 (2012)
- W. G. Bade, "Amenability and weak amenability for Beurling and Lipschitz algebras", Proc. London Math. Soc. (3), 55(2), pp.359~377 (1987)
- H. G. Dales, "Quasianalytic Banach function algebras", J. Funct. Anal, 13(1), pp.28~50 (1973)
- T. W. Gamelin, "Uniform algebras" (1984), Chelsea Publishing company
- T. G. Honary, "Relations between Banach function algebras and their uniform closures", Proc. Amer. Math. Soc, 109, pp.337~342 (1990)
- T. G. Honary, "Approximations in Lipschitz algebras of infinitely differentiable functions", Bull. Korean Math. Soc, 36, pp.629~636 (1999)
- T. G. Honary, "On the maximal ideal space of extended analytic Lipschitz algebras", Quaest. Math, 30, pp.349~353 (2007)
- T. G. Honary, "Uniform approximation by polynomial, rational and analytic functions", Bull. Austral. Math. Soc., 77, pp.389~399 (2008)
- D. R. Sherbert, "The structure of ideals and point derivations in Banach algebras of Lipschitz functions", Trans. Amer. Math. Soc, 111, pp.240~272 (1964)
- N. Weaver, "Lipschitz algebras" (1999), World Scientific Publishing Co