On the spectrum of A(Ω) and H ∞ ( Ω )

Urban Cegrell

Annales Polonici Mathematici (1993)

  • Volume: 58, Issue: 2, page 193-199
  • ISSN: 0066-2216

Abstract

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We study some properties of the maximal ideal space of the bounded holomorphic functions in several variables. Two examples of bounded balanced domains are introduced, both having non-trivial maximal ideals.

How to cite

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Urban Cegrell. "On the spectrum of A(Ω) and $H^∞(Ω)$." Annales Polonici Mathematici 58.2 (1993): 193-199. <http://eudml.org/doc/262439>.

@article{UrbanCegrell1993,
abstract = {We study some properties of the maximal ideal space of the bounded holomorphic functions in several variables. Two examples of bounded balanced domains are introduced, both having non-trivial maximal ideals.},
author = {Urban Cegrell},
journal = {Annales Polonici Mathematici},
keywords = {bounded analytic function; spectrum; Gleason problem; balanced domain; algebra of bounded holomorphic functions; balanced -domains; pseudoconvex domains},
language = {eng},
number = {2},
pages = {193-199},
title = {On the spectrum of A(Ω) and $H^∞(Ω)$},
url = {http://eudml.org/doc/262439},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Urban Cegrell
TI - On the spectrum of A(Ω) and $H^∞(Ω)$
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 2
SP - 193
EP - 199
AB - We study some properties of the maximal ideal space of the bounded holomorphic functions in several variables. Two examples of bounded balanced domains are introduced, both having non-trivial maximal ideals.
LA - eng
KW - bounded analytic function; spectrum; Gleason problem; balanced domain; algebra of bounded holomorphic functions; balanced -domains; pseudoconvex domains
UR - http://eudml.org/doc/262439
ER -

References

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  1. [1] U. Cegrell, Representing measures in the spectrum of H ∞ ( Ω ) , in: Complex Analysis, Proc. Internat. Workshop, Wuppertal 1990, K. Diederich (ed.), Aspects of Math. E17, Vieweg, 1991, 77-80. 
  2. [2] J. E. Fornæss and N. Øvrelid, Finitely generated ideals in A(Ω), Ann. Inst. Fourier (Grenoble) 33 (2) (1983), 77-85. Zbl0489.32013
  3. [3] T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. Zbl0213.40401
  4. [4] T. W. Gamelin, Uniform Algebras and Jensen Measures, Cambridge Univ. Press, 1978. 
  5. [5] M. Hakim et N. Sibony, Spectre de A(Ω̅ ) pour les domaines bornés faiblement pseudoconvexes réguliers, J. Funct. Anal. 37 (1980), 127-135. Zbl0441.46044
  6. [6] J. J. Kohn, Global regularity for ∂̅ on weakly pseudo-convex manifolds, Trans. Amer. Math. Soc. 181 (1973), 273-292. Zbl0276.35071
  7. [7] A. Noell, The Gleason problem for domains of finite type, Complex Variables 4 (1985), 233-241. Zbl0535.32009
  8. [8] M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer, 1986. Zbl0591.32002
  9. [9] N. Sibony, Prolongement analytique des fonctions holomorphes bornées, in: Sém. Pierre Lelong 1972-73, Lecture Notes in Math. 410, Springer, 1974, 44-66. 
  10. [10] J. Siciak, Balanced domains of holomorphy of type H ∞ , Mat. Vesnik 37 (1985), 134-144. Zbl0575.32009
  11. [11] N. Øvrelid, Generators of the maximal ideals of A(D̅), Pacific J. Math. 39 (1971), 219-223. Zbl0231.46090

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