A spectral Schwarz lemma
type: Item
instance of: scholarly article
title: A spectral Schwarz lemma
zbMATH Open document ID: 1194.30041
DOI: 10.4171/RLM/527
author: Edoardo Vesentini
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2010-09-19T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: Summary: The classical Schwarz lemma for any scalar-valued holomorphic function \(h\) mapping the open unit disc \(\Delta \subset \mathbb{C}\) into itself is generalized, replacing \(h\) by a holomorphic map \(f\) of \(\Delta\) into a unital associative Banach algebra \({\mathcal A}\), and \(| h(z) |\) by the spectral radius of \(f(z) (z \in \Delta)\). If \({\mathcal A} = {\mathcal L}({\mathcal H})\) and \({\mathcal H}\) is a complex Hilbert space, the behaviour of the numerical radius of \(f(z)\) is also investigated.
Mathematics Subject Classification ID: 30E25
zbMATH DE Number: 5787945
zbMATH Keywords: Banach algebra
zbMATH Keywords: spectrum
zbMATH Keywords: spectral radius
zbMATH Keywords: numerical radius
MaRDI profile type: Publication
Wikidata QID: Q124984723
cites work: Q5561452
cites work: Q5727906
cites work: Sur les ensembles pseudoconcaves
cites work: Q4759691
cites work: Analytic set-valued functions and spectra
cites work: Maximum theorems for vector valued holomorphic functions
cites work: Caratheodory distances and Banach algebras
cites work: Sur une uniformite des surfaces constantes d'une fonction entière de deux variables complexes
OpenAlex ID: W2075772289
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description: scientific article; zbMATH DE number 5787945