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Sbornik: Mathematics, 2011, Volume 202, Issue 5, Pages 721–737
DOI: https://doi.org/10.1070/SM2011v202n05ABEH004163
(Mi sm7668)
 

This article is cited in 12 scientific papers (total in 12 papers)

Fredholm and spectral properties of Toeplitz operators on $H^p$ spaces over ordered groups

A. R. Mirotin

Francisk Skorina Gomel State University
References:
Abstract: We consider Toeplitz operators on the spaces $H^p(G)$, $1< p<\infty$, associated with a compact connected Abelian group $G$ whose character group is ordered and, in the case of total order, prove a theorem on the Fredholm index for those operators which have continuous symbols which generalizes the classical Gohberg-Krein theorem. The results thus obtained are applied to the spectral theory of Toeplitz operators and examples where the index is evaluated explicitly are considered.
Bibliography: 22 titles.
Keywords: Toeplitz operator, Fredholm operator, Fredholm index, essential spectrum, ordered Abelian group.
Received: 15.12.2009 and 29.06.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 5, Pages 101–116
DOI: https://doi.org/10.4213/sm7668
Bibliographic databases:
Document Type: Article
UDC: 517.983.23+517.984.5
MSC: 43A15, 47B35
Language: English
Original paper language: Russian
Citation: A. R. Mirotin, “Fredholm and spectral properties of Toeplitz operators on $H^p$ spaces over ordered groups”, Mat. Sb., 202:5 (2011), 101–116; Sb. Math., 202:5 (2011), 721–737
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/sm7668
  • https://doi.org/10.1070/SM2011v202n05ABEH004163
  • https://www.mathnet.ru/eng/sm/v202/i5/p101
  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
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    Abstract page:543
    Russian version PDF:211
    English version PDF:12
    References:78
    First page:18
     
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