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Mat. Sb., 2011, Volume 202, Number 5, Pages 101–116 (Mi msb7668)  

This article is cited in 9 scientific papers (total in 9 papers)

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

A. R. Mirotin

Francisk Skorina Gomel State University

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.

DOI: https://doi.org/10.4213/sm7668

Full text: PDF file (568 kB)
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English version:
Sbornik: Mathematics, 2011, 202:5, 721–737

Bibliographic databases:

UDC: 517.983.23+517.984.5
MSC: 43A15, 47B35
Received: 15.12.2009 and 29.06.2010

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. V. Dyba, “Teorema Nekhari na kompaktnykh abelevykh gruppakh s lineino uporyadochennoi gruppoi kharakterov”, PFMT, 2011, no. 3(8), 57–60  mathnet
    2. A. R. Mirotin, R. S. Melnikov, “Teoremy o spektralnykh vklyucheniyakh dlya operatorov Tëplitsa v prostranstvakh Khardi $H_p$ nad kompaktnoi abelevoi gruppoi”, Izvestiya Gomelskogo gosudarstvennogo universiteta im. F. Skoriny, 2013, no. 6, 29–33  zmath  elib
    3. R. V. Dyba, A. R. Mirotin, “Funktsii ogranichennoi srednei ostsillyatsii i gankelevy operatory na kompaktnykh abelevykh gruppakh”, Tr. IMM UrO RAN, 20, no. 2, 2014, 135–144  mathnet  mathscinet  elib
    4. V. V. Kisil, “Calculus of operators: covariant transform and relative convolutions”, Banach J. Math. Anal., 8:2 (2014), 156–184  crossref  mathscinet  zmath  isi  scopus
    5. A. R. Mirotin, “On the essential spectrum of $\lambda$-Toeplitz operators over compact Abelian groups”, J. Math. Anal. Appl., 424:2 (2015), 1286–1295  crossref  mathscinet  zmath  isi  scopus
    6. A. R. Mirotin, R. V. Dyba, “O konechnomernykh i yadernykh gankelevykh operatorakh v prostranstvakh Khardi $H^2$ na kompaktnykh abelevykh gruppakh”, PFMT, 2015, no. 4(25), 74–79  mathnet
    7. A. R. Mirotin, E. Yu. Kuzmenkova, “O gankelevykh operatorakh, assotsiirovannykh s lineino uporyadochennymi abelevymi gruppami”, Tr. IMM UrO RAN, 22, no. 4, 2016, 201–214  mathnet  crossref  mathscinet  elib
    8. Mirotin A.R., “on the General Form of Linear Functionals on the Hardy Spaces H-1 Over Compact Abelian Groups and Some of Its Applications”, Indag. Math.-New Ser., 28:2 (2017), 451–462  crossref  mathscinet  zmath  isi  scopus
    9. Blecher D.P., Labuschagne L.E., “On Vector-Valued Characters For Noncommutative Function Algebras”, Complex Anal. Oper. Theory, 14:2 (2020), 31  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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