Local objects in the theory of Toeplitz operators
type: Item
instance of: scholarly article
title: Local objects in the theory of Toeplitz operators
zbMATH Open document ID: 0609.47038
DOI: 10.1007/BF01195809
author: B. Silbermann
published in: Integral Equations and Operator Theory
publication date: 1986-01-01T00:00:00Z
review text: R. Douglas associated with every Toeplitz operator a family of local Toeplitz opertors to study the Fredholm theory of Toeplitz operators. In the present paper local objects are introduced which can be used to study approximation of block Toeplitz operators by their finite sections or by their harmonic extension. So it turns out that there is a unified approach to quite different problems concerning Toeplitz operators, which, undoubtedly, provides new insights into the common features but also into the significant differences between various ''Toeplitz-like results''. The method developed in this paper yields new results on Fredholmness, harmonic approximation, and finite sections of block Toeplitz operators (involving, in particular, a new first Szegö limit theorem) and offers a possibility of computing the index of block Toeplitz operators generated by matrix functions that are locally sectorial over QC.
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 3985982
zbMATH Keywords: Banach algebra techniques
zbMATH Keywords: local Toeplitz opertors
zbMATH Keywords: Fredholm theory of Toeplitz operators
zbMATH Keywords: approximation of block Toeplitz operators by their finite sections or by their harmonic extension
zbMATH Keywords: harmonic approximation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3985982