Generators of the maximal ideals of A(D)

Nils Øvrelid

Vol. 39 (1971), No. 1, 219–223

DOI: 10.2140/pjm.1971.39.219

Abstract

Let A = A(D) be the sup norm algebra of functions continuous in D and holomorphic in D, where D is a bounded, strictly pseudoconvex domain in Cⁿ. This paper gives necessary and sufficient local conditions that a subfamily of A generates the maximal ideal ℳ_w(D) of functions in A vanishing at w ∈D. In particular, it shows that ℳ_w(D) is generated by z₁ − w₁,⋯,z_n − w_n when W ∈ D.

Mathematical Subject Classification 2000

Primary: 32E30

Secondary: 46J10

Milestones

Received: 6 August 1970

Published: 1 October 1971