Extremal functions as divisors for kernels of Toeplitz operators.
type: Item
instance of: scholarly article
title: Extremal functions as divisors for kernels of Toeplitz operators.
zbMATH Open document ID: 1060.30046
DOI: 10.1016/S0022-1236(03)00074-0
author: A. Hartmann
author: Kristian Seip
published in: Journal of Functional Analysis
publication date: 2003-09-04T00:00:00Z
review text: The paper studies the extremal functions for kernels of Toeplitz operators on the classical Hardy spaces \(H^p\) when \(1<p<\infty\). Such kernels are special cases of the so-called nearly invariant subspaces of the backward shift. It is a theorem of Hitt that the extremal function of a nearly invariant subspace of the backward shift on \(H^2\) acts as an isometric divisor. The present paper shows that the extremal function of the kernel of a Toeplitz operator on \(H^p\) is a contractive divisor when \(p<2\) and an expansive divisor when \(p>2\), modulo \(p\)-dependent multiplicative constants. Examples are also supplied to show that the extremal function is generally not expansive when \(p<2\) and not contractive when \(p<2\) and not contractive when \(p>2\).
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 1974802
zbMATH Keywords: Toeplitz operators
zbMATH Keywords: Extremal functions
zbMATH Keywords: Invariant subspaces with respect to the backward shift
zbMATH Keywords: Nearly invariant subspaces
zbMATH Keywords: Carleson measures
reviewed by: Kehe Zhu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1974802