Trudy Matematicheskogo Instituta imeni V.A. Steklova
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 306, Pages 227–234
DOI: https://doi.org/10.4213/tm4004 (Mi tm4004) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Quantum Calculus and Ideals in the Algebra of Compact Operators

A. G. Sergeev

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (170 kB) Citations (1)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tm4004
Abstract: One of the goals of noncommutative geometry is to translate the basic notions of analysis into the language of Banach algebras. This translation is based on the quantization procedure. The arising operator calculus is called, following Connes, the quantum calculus. In this paper we give several assertions from this calculus concerning the interpretation of Schatten ideals of compact operators in a Hilbert space in terms of function theory. The main focus is on the case of Hilbert–Schmidt operators.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00117
16-52-12012
18-51-05009
The work was supported in part by the Russian Foundation for Basic Research, project nos. 16-01-00117, 16-52-12012, and 18-51-05009.
Received: August 16, 2018
Revised: August 25, 2018
Accepted: March 22, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 306, Pages 212–219
DOI: https://doi.org/10.1134/S0081543819050183
Bibliographic databases:
Document Type: Article
UDC: 514.7+517.98
Language: Russian
Citation: A. G. Sergeev, “Quantum Calculus and Ideals in the Algebra of Compact Operators”, Mathematical physics and applications, Collected papers. In commemoration of the 95th anniversary of Academician Vasilii Sergeevich Vladimirov, Trudy Mat. Inst. Steklova, 306, Steklov Math. Inst. RAS, Moscow, 2019, 227–234; Proc. Steklov Inst. Math., 306 (2019), 212–219
Citation in format AMSBIB
\Bibitem{Ser19}
\by A.~G.~Sergeev
\paper Quantum Calculus and Ideals in the Algebra of Compact Operators
\inbook Mathematical physics and applications
\bookinfo Collected papers. In commemoration of the 95th anniversary of Academician Vasilii Sergeevich Vladimirov
\serial Trudy Mat. Inst. Steklova
\yr 2019
\vol 306
\pages 227--234
\publ Steklov Math. Inst. RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4004}
\crossref{https://doi.org/10.4213/tm4004}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4040777}
\elib{https://elibrary.ru/item.asp?id=43228739}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2019
\vol 306
\pages 212--219
\crossref{https://doi.org/10.1134/S0081543819050183}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000511670100018}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85077373923}
Linking options:
  • https://www.mathnet.ru/eng/tm4004
  • https://doi.org/10.4213/tm4004
  • https://www.mathnet.ru/eng/tm/v306/p227
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Statistics & downloads:
    Abstract page:332
    Full-text PDF :31
    References:23
    First page:10
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024