# On the spectrum of A(Ω) and ${H}^{\infty}\left(\Omega \right)$

Annales Polonici Mathematici (1993)

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

## Access Full Article

top## Abstract

top## How to cite

topUrban 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

top- [1] U. Cegrell, Representing measures in the spectrum of ${H}^{\infty}\left(\Omega \right)$, in: Complex Analysis, Proc. Internat. Workshop, Wuppertal 1990, K. Diederich (ed.), Aspects of Math. E17, Vieweg, 1991, 77-80.
- [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] T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. Zbl0213.40401
- [4] T. W. Gamelin, Uniform Algebras and Jensen Measures, Cambridge Univ. Press, 1978.
- [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] J. J. Kohn, Global regularity for ∂̅ on weakly pseudo-convex manifolds, Trans. Amer. Math. Soc. 181 (1973), 273-292. Zbl0276.35071
- [7] A. Noell, The Gleason problem for domains of finite type, Complex Variables 4 (1985), 233-241. Zbl0535.32009
- [8] M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer, 1986. Zbl0591.32002
- [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] J. Siciak, Balanced domains of holomorphy of type ${H}^{\infty}$, Mat. Vesnik 37 (1985), 134-144. Zbl0575.32009
- [11] N. Øvrelid, Generators of the maximal ideals of A(D̅), Pacific J. Math. 39 (1971), 219-223. Zbl0231.46090

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.