Generalized rational convexity in Banach algebras

Gustavo Corach and Daniel Suarez

Vol. 140 (1989), No. 1, 35–51

DOI: 10.2140/pjm.1989.140.35

Abstract

Let A be a complex commutative Banach algebra with identity and let F be a closed subset of its spectrum X(A). There are several hulls, associated with F, which are useful in the study of approximation, interpolation and separation problems: the polynomially and rationally convex hulls are the most popular, the A-convex hull has also been considered and there are also holomorphically convex hulls. In this paper we introduce a family of hulls, denoted by R_n(F), and we study some relations between these hulls and several known objects and invariants in commutative Banach algebras.

Mathematical Subject Classification 2000

Primary: 46J05

Secondary: 46J10, 46J40

Milestones

Received: 15 June 1987

Revised: 10 September 1988

Published: 1 November 1989