Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

The Maximal Ideal Space of Extended Differentiable Lipschitz Algebras

  • Received : 2018.05.14
  • Accepted : 2018.12.26
  • Published : 2020.03.31
Download PDF
⟨ Previous Next ⟩

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.

Keywords

Acknowledgement

Supported by : Urmia University

This work was supported by Urmia University.

References

  1. M. Abtahi, Normed algebras of infinitely differentiable Lipschitz functions, Quaest. Math., 35(2)(2012), 195-202. https://doi.org/10.2989/16073606.2012.696855
  2. W. G. Bade, P. C. Curtis and H. G. Dales, Amenability and weak amenability for Beurling and Lipschitz algebras, Proc. London Math. Soc. (3), 55(2)(1987), 359-377.
  3. H. G. Dales and A. M. Davie, Quasianalytic Banach function algebras, J. Funct. Anal., 13(1)(1973), 28-50. https://doi.org/10.1016/0022-1236(73)90065-7
  4. T. W. Gamelin, Uniform algebras, Chelsea Publishing company, 1984.
  5. T. G. Honary, Relations between Banach function algebras and their uniform closures, Proc. Amer. Math. Soc., 109(1990), 337-342. https://doi.org/10.1090/S0002-9939-1990-1007499-4
  6. T. G. Honary and H. Mahyar, Approximations in Lipschitz algebras of infinitely differentiable functions, Bull. Korean Math. Soc., 36(1999), 629-636.
  7. T. G. Honary and S. Moradi, On the maximal ideal space of extended analytic Lipschitz algebras, Quaest. Math., 30(2007), 349-353. https://doi.org/10.2989/16073600709486204
  8. T. G. Honary and S. Moradi, Uniform approximation by polynomial, rational and analytic functions, Bull. Austral. Math. Soc., 77(2008), 389-399.
  9. D. R. Sherbert, The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc., 111(1964), 240-272. https://doi.org/10.1090/S0002-9947-1964-0161177-1
  10. N. Weaver, Lipschitz algebras, World Scientific Publishing Co, 1999.