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 Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 4, Pages 201–214 (Mi timm1366)

On Hankel operators associated with linearly ordered abelian groups

A. R. Mirotin, E. Yu. Kuz'menkova

Gomel State University named after Francisk Skorina

Abstract: We consider two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups. Criteria for the boundedness and compactness of these operators are given, in particular, in terms of functions of bounded mean oscillation. It is proved that the generalized Hankel operators are non-Fredholm. Some applications to the theory of Toeplitz operators on groups are given.

Keywords: Hankel operator, integral Hankel operator, Fredholm operator, compact operator, bounded mean oscillation, linearly ordered abelian group, compact abelian group, Toeplitz operator.

 Funding Agency Grant Number National Academy of Sciences of Belarus, Ministry of Education of the Republic of Belarus 20160825

DOI: https://doi.org/10.21538/0134-4889-2016-22-4-201-214

Full text: PDF file (257 kB)
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Bibliographic databases:

UDC: 517.986.62
MSC: 47B35, 43A17

Citation: A. R. Mirotin, E. Yu. Kuz'menkova, “On Hankel operators associated with linearly ordered abelian groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 4, 2016, 201–214

Citation in format AMSBIB
\Bibitem{MirKuz16} \by A.~R.~Mirotin, E.~Yu.~Kuz'menkova \paper On Hankel operators associated with linearly ordered abelian groups \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2016 \vol 22 \issue 4 \pages 201--214 \mathnet{http://mi.mathnet.ru/timm1366} \crossref{https://doi.org/10.21538/0134-4889-2016-22-4-201-214} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3590934} \elib{https://elibrary.ru/item.asp?id=27350138}