Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The Structure of Maximal Ideal Space of Certain Banach Algebras of Vector-valued Functions

  • Shokri, Abbas Ali (Department of Mathematics, Ahar Branch, Islamic Azad University) ;
  • Shokri, Ali (Department of Mathematics, Faculty of Basic Science, University of Maragheh)
  • Received : 2011.04.25
  • Accepted : 2013.03.27
  • Published : 2014.06.23
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Abstract

Let X be a compact metric space, B be a unital commutative Banach algebra and ${\alpha}{\in}(0,1]$. In this paper, we first define the vector-valued (B-valued) ${\alpha}$-Lipschitz operator algebra $Lip_{\alpha}$ (X, B) and then study its structure and characterize of its maximal ideal space.

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References

  1. W. G. Bade, P. C. Curtis and Dales, H. G., Amenability and weak amenability for Berurling and Lipschitz algebras, Proc. London. Math. Soc. (3), 55(2)(1987), 359-377.
  2. H. X. Cao, J. H. Zhang, and Z. B., Xu, Characterizations and extensions of Lipschitz-$\alpha$ operators, Acta Mathematica Sinica, English Series, 22(2006), 671-678.
  3. A. Ebadian, Prime ideals in Lipschitz algebras of finite differentable function, Honam Math. J., 22(2000), 21-30.
  4. A. Ebadian and A. A. Shokri, On the Lipschitz operator algebras, Archivum mathe-maticum (BRNO), 45(2)(2009), 213-222.
  5. T. G. Honary and H. Mahyar, Approximation in Lipschitz algebras, Quest. Math., 23(2000), 13-19. https://doi.org/10.2989/16073600009485953
  6. J. A. Johnson, Lipschitz spaces, Pacific J. Math, 51(1974), 177-186. https://doi.org/10.2140/pjm.1974.51.177
  7. V. Runde, Lectures on Amenability, Springer, 2002.
  8. D. R. Sherbert, Banach algebras of Lipschitz functions, Pacfic J. Math, 13(1963), 1387-1399. https://doi.org/10.2140/pjm.1963.13.1387
  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., Inc., River Edge, NJ, 1999.
  11. N. Weaver, Subalgebras of little Lipschitz algebras, Pacfic J. Math., 173(1996), 283-293. https://doi.org/10.2140/pjm.1996.173.283