Iversen’s theorem and fiber algebras

Theodore William Gamelin

Vol. 46 (1973), No. 2, 389–414

DOI: 10.2140/pjm.1973.46.389

Abstract

The main theorem asserts that S_ζ(D) = S(D) ∩ℳ_ζ(D), where D is a polydomain in Cⁿ,S(D) is the Shilov boundary of H^∞(D),ζ is an essential distinguished boundary point of D,ℳ_ζ(D) is the fiber over ζ of the maximal ideal space of H^∞(D), and S_ζ(D) is the Shilov boundary of the fiber algebra. The main theorem includes Iversen’s theorem for polydomains.

Mathematical Subject Classification 2000

Primary: 46J15

Secondary: 32E25

Milestones

Received: 20 April 1972

Revised: 26 October 1972

Published: 1 June 1973