Fredholm composition operators on algebras of analytic functions on Banach spaces
type: Item
instance of: scholarly article
title: Fredholm composition operators on algebras of analytic functions on Banach spaces
zbMATH Open document ID: 1190.47027
author: Pablo Galindo
author: T. W. Gamelin
author: Mikael Lindström
published in: Journal of Functional Analysis
publication date: 2010-02-24T00:00:00Z
review text: Let \(E\) be a complex Banach space with open unit ball \(B_E\), and let \(\varphi:B_E\rightarrow B_E\) be a nonconstant analytic map. The composition operator \(C_\varphi\) is defined by \(C_\varphi(f)=f\circ \varphi\) and acts on the uniform algebra of bounded analytic functions on \(B_E\) endowed with the norm \(\| f\|=\sup_{x\in B_E}|f(x)|\). Under the additional assumption that \(E\) possesses the approximation property, it is proved that Fredholm composition operators are invertible and arise from analytic automorphisms of the ball.
reviewed by: Vladimir S. Pilidi
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 46E50
Mathematics Subject Classification ID: 47A53
zbMATH DE Number: 5674480
zbMATH Keywords: composition operator
zbMATH Keywords: Fredholm operator
zbMATH Keywords: bounded analytic function
MaRDI profile type: Publication
full work available at URL: j.jfa.2009.10.020
OpenAlex ID: W1998551837
cites work: Q5748432
cites work: Multiplication operators on Bergman spaces.
cites work: Q4487417
cites work: A Uniform Algebra of Analytic Functions on a Banach Space
cites work: Q3688914
cites work: On biholomorphy in infinite dimensions
cites work: Q4402891
cites work: Q4257163
cites work: Q3254057
cites work: Interpolating sequences for bounded analytic functions
cites work: COMPOSITION OPERATORS ON UNIFORM ALGEBRAS AND THE PSEUDOHYPERBOLIC METRIC
cites work: Embedding Riemann surfaces in maximal ideal spaces
cites work: Q4309440
cites work: Fredholm composition operators on spaces of holomorphic functions
cites work: Fredholm composition operators
cites work: Complex homomorphisms of the algebras of holomorphic functions on Frechet spaces
cites work: Spectral theory of linear operators and spectral systems in Banach algebras
DOI: 10.1016/J.JFA.2009.10.020
description: scientific article; zbMATH DE number 5674480