Jensen measures of uniform algebras
type: Item
instance of: scholarly article
title: Jensen measures of uniform algebras
zbMATH Open document ID: 0655.46046
DOI: 10.1007/BF02766206
published in: Israel Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: It is proved that Jensen measures are the maximal measures for certain systems of Jensen measures. More precisely: Let A be a uniform algebra with maximal ideal space. The cone of A-subharmonic functions in \(C_ R(Y)\) defines a partial order \(\prec\) among positive measures on \(M^+(Y)\). For each \(p\in Y\), let \(F_ p\) denote the set of compact subsets of Y containing p. A subset \(\{\lambda_ G| G\in F_ p\}\) of \(M^+(Y)\) is called a consistent system if it satisfies the following conditions: (a) \(\lambda_ G\) is a Jensen measure for p with support contained in G, (b) if \(F\subset G\) then \(\lambda_ F\prec \lambda_ G,\) (c) if \(F\in G\) then \(\lambda_ G(g)\leq \lambda_ F(g)\) for all non- negative \(g\in C_ R(Y)\) such that \(g=0\) on \(G\setminus F.\) There is a unique measure \(\lambda_ Y\) which is maximal in \(\{\lambda_ G| G\in F_ p\}\). A terminal measure is a measure which is maximal in some consistent system. The main result of this paper states that every Jensen measure for A is a terminal measure.
Mathematics Subject Classification ID: 46J10
zbMATH DE Number: 4069592
zbMATH Keywords: Jensen measures
zbMATH Keywords: maximal measures
zbMATH Keywords: uniform algebra
zbMATH Keywords: maximal ideal space
zbMATH Keywords: cone of A-subharmonic functions
zbMATH Keywords: consistent system
zbMATH Keywords: terminal measure
author: Cho-ichiro Matsuoka
reviewed by: E. Briem
MaRDI profile type: Publication
cites work: Q5611281
cites work: Analytic functions of several Banach algebra elements
cites work: Holomorphic completions, analytic continuation, and the interpolation of semi-norms
cites work: On a Generalized Dirichlet Problem for Plurisubharmonic Functions and Pseudo-Convex Domains. Characterization of Silov Boundaries
cites work: A Maximal Function Characterization of the Class H p
cites work: Comparaison, des mesures portées par un ensemble convexe compact
cites work: Q5662251
cites work: Q5822308
cites work: \(H^p\) spaces of several variables
cites work: Q5615632
cites work: Q3851127
cites work: Jensen measures and maximal functions of uniform algebras
cites work: A certain class of Jensen measures for uniform algebras
cites work: M. Riesz's theorem in the abstract Hardy space theory
description: scientific article; zbMATH DE number 4069592