The support points of the unit ball in Bloch space
type: Item
instance of: scholarly article
title: The support points of the unit ball in Bloch space
zbMATH Open document ID: 0808.46075
author: Mario Bonk
published in: Journal of Functional Analysis
publication date: 1994-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/2027.42/31411
review text: Let \(H({\mathbf D})\) be the topological vector space of all functions \(F\) holomorphic in the unit disc \({\mathbf D}\). The author considers the compact convex subset \[ \widetilde{\mathcal B}_ 1= \{F\in H({\mathbf D}): F(0)= 0\land | F'(z)|(1- | z|^ 2)\leq 1\text{ for }z\in {\mathbf D}\} \] of \(H({\mathbf D})\) and shows that \(G\in \widetilde{\mathcal B}_ 1\) is a support point of \(\widetilde{\mathcal B}_ 1\) if and only if \[ \Lambda(G)= \{z\in {\mathbf D}: | G'(z)|(1-| z|^ 2)= 1\}\neq\emptyset. \] This is an application of a more general result which is concerned with the maximization of continuous linear functionals on a set \({\mathcal K}_ 1\) related to \(\widetilde{\mathcal B}_ 1\).
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 635903
zbMATH Keywords: support points of the unit ball in Bloch space
zbMATH Keywords: compact convex subset
zbMATH Keywords: maximization of continuous linear functionals
MaRDI profile type: Publication
OpenAlex ID: W2071930078
DOI: 10.1006/JFAN.1994.1091
Recommended article: Q4262615
Recommended article: Bloch space in the unit ball of $\mathbb {C}^{n}$
Recommended article: Q4354138
Recommended article: The pointwise multipliers of \(p\)-Bloch space in the unit ball of \(\mathbb{C}^n\)
Recommended article: Bloch type spaces on the unit ball of a Hilbert space
Recommended article: Q3473368
Recommended article: The Bloch space on the unit ball of a Hilbert space: maximality and multipliers
Recommended article: Extreme points and support points of harmonic \(\alpha\)-Bloch mappings
Recommended article: Q3764430
Recommended article: Q4710670
description: scientific article; zbMATH DE number 635903