×

zbMATH — the first resource for mathematics

The Gleason problem for \(\mathbb A^k(\Omega)\), \(\mathbb H^k(\Omega)\), \(\text{Lip}_{k=\varepsilon} (\Omega)\). (English) Zbl 1037.32008
Let \(\Omega\) be a domain in \(\mathbb C^n\) and \(\mathbb A(\Omega)\) be the algebra of functions holomorphic in \(\Omega\) and continuous on the closure of \(\Omega\).
The author compares the maximal ideal \(m_p\) in \(\mathbb A(\Omega)\) given by all the functions vanishing at a point \(p\in \Omega\) to the ideal generated by \(z_1-p_1,\dots, z_n- p_n\).
MSC:
32A38 Algebras of holomorphic functions of several complex variables
32B05 Analytic algebras and generalizations, preparation theorems
46E25 Rings and algebras of continuous, differentiable or analytic functions
PDF BibTeX XML Cite
Full Text: EuDML