Abstract:
We consider Toeplitz operators on the spaces Hp(G), 1<p<∞, 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.
\Bibitem{Mir11}
\by A.~R.~Mirotin
\paper Fredholm and spectral properties of Toeplitz operators on $H^p$ spaces over ordered groups
\jour Sb. Math.
\yr 2011
\vol 202
\issue 5
\pages 721--737
\mathnet{http://mi.mathnet.ru/eng/sm7668}
\crossref{https://doi.org/10.1070/SM2011v202n05ABEH004163}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2841520}
\zmath{https://zbmath.org/?q=an:1228.43003}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2011SbMat.202..721M}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000294703200006}
\elib{https://elibrary.ru/item.asp?id=19066279}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051731797}
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:
A. Mirotin, “μ-Hankel operators on compact Abelian groups”, Anal Math, 49:2 (2023), 617
A. R. Mirotin, “Hausdorff operators on compact abelian groups”, Mathematische Nachrichten, 296:9 (2023), 4108
A. R. Mirotin, “Compact Hankel operators over compact Abelian groups”, St. Petersburg Math. J., 33:3 (2022), 569–584
Blecher D.P., Labuschagne L.E., “On Vector-Valued Characters For Noncommutative Function Algebras”, Complex Anal. Oper. Theory, 14:2 (2020), 31
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
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
A. R. Mirotin, “On the essential spectrum of λ-Toeplitz operators over compact Abelian groups”, J. Math. Anal. Appl., 424:2 (2015), 1286–1295
A. R. Mirotin, R. V. Dyba, “O konechnomernykh i yadernykh gankelevykh operatorakh v prostranstvakh Khardi H2 na kompaktnykh abelevykh gruppakh”, PFMT, 2015, no. 4(25), 74–79
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
V. V. Kisil, “Calculus of operators: covariant transform and relative convolutions”, Banach J. Math. Anal., 8:2 (2014), 156–184
A. R. Mirotin, R. S. Melnikov, “Teoremy o spektralnykh vklyucheniyakh dlya operatorov Tëplitsa v prostranstvakh Khardi Hp nad kompaktnoi abelevoi gruppoi”, Izvestiya Gomelskogo gosudarstvennogo universiteta im. F. Skoriny, 2013, no. 6, 29–33
R. V. Dyba, “Teorema Nekhari na kompaktnykh abelevykh gruppakh s lineino uporyadochennoi gruppoi kharakterov”, PFMT, 2011, no. 3(8), 57–60
Citation in format AMSBIB
Contact us: