Functional calculus under the Tadmor--Ritt condition, and free interpolation by polynomials of a given degree
type: Item
instance of: scholarly article
title: Functional calculus under the Tadmor--Ritt condition, and free interpolation by polynomials of a given degree
zbMATH Open document ID: 1065.47015
author: Pascale Vitse
published in: Journal of Functional Analysis
publication date: 2004-08-16T00:00:00Z
review text: Let \(T: X \to X\) be a bounded operator in a Banach space \(X\). Suppose that \(T\) satisfies the Tadmor--Ritt condition (TR): \(\| (zI-T)^{-1} \| \leq C | z-1 |^{-1}\) for all \(| z| >1\). The problem under consideration is to estimate the rate of growth of the following constant: \(C_T (n)=\sup \{ \| p(T)\|: \text{ {deg}}(p)\leq n, \| p \|_{\infty} \leq 1\}\). The author proves that \(C_T(n) \leq (C+1) \log (e^2 n), n \geq 1\). Moreover, there exists an operator \(T\) satisfying (TR) with a constant \(C \leq \pi/2+1\) and such that \(C_T(n) \geq 1/2540 \log(e^2 n)\) for all \(n \geq 1\).
reviewed by: Mikhail Yu. Kokurin
Mathematics Subject Classification ID: 47A60
zbMATH DE Number: 2091738
zbMATH Keywords: Tadmor and Ritt conditions
zbMATH Keywords: functional calculus
zbMATH Keywords: Cauchy-Stieltjes integrals
zbMATH Keywords: Carleson type free interpolation by polynomials
MaRDI profile type: Publication
full work available at URL: j.jfa.2003.08.002
OpenAlex ID: W2090827184
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DOI: 10.1016/J.JFA.2003.08.002
description: scientific article; zbMATH DE number 2091738