Funktsional'nyi Analiz i ego Prilozheniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find




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

Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 2, Pages 91–94
DOI: https://doi.org/10.4213/faa112 (Mi faa112) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Brief communications

When Is a Sum of Partial Reflections Equal to a Scalar Operator?

A. S. Mellit, V. I. Rabanovich, Yu. S. Samoilenko

Institute of Mathematics, Ukrainian National Academy of Sciences
Full-text PDF (157 kB) Citations (7)
References:
PDF
HTML
DOI: https://doi.org/10.4213/faa112
Abstract: We describe the set $\widetilde{W}_n$ of values of the parameter $\alpha\in\mathbb{R}$ for which there exists a Hilbert space $H$ and $n$ partial reflections $A_1,\dots,A_n$ (self-adjoint operators such that $A_k^3=A_k$ or, which is the same, self-adjoint operators whose spectra belong to the set $\{-1,0,1\}$) whose sum is equal to the scalar operator $\alpha I_H$.
Keywords: projection, reflection, partial reflection, self-adjoint operator, *-representation.
Received: 12.02.2003
English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 2, Pages 157–160
DOI: https://doi.org/10.1023/B:FAIA.0000034047.27498.51
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: A. S. Mellit, V. I. Rabanovich, Yu. S. Samoilenko, “When Is a Sum of Partial Reflections Equal to a Scalar Operator?”, Funktsional. Anal. i Prilozhen., 38:2 (2004), 91–94; Funct. Anal. Appl., 38:2 (2004), 157–160
Citation in format AMSBIB
\Bibitem{MelRabSam04}
\by A.~S.~Mellit, V.~I.~Rabanovich, Yu.~S.~Samoilenko
\paper When Is a Sum of Partial Reflections Equal to a Scalar Operator?
\jour Funktsional. Anal. i Prilozhen.
\yr 2004
\vol 38
\issue 2
\pages 91--94
\mathnet{http://mi.mathnet.ru/faa112}
\crossref{https://doi.org/10.4213/faa112}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2086631}
\zmath{https://zbmath.org/?q=an:1069.47021}
\transl
\jour Funct. Anal. Appl.
\yr 2004
\vol 38
\issue 2
\pages 157--160
\crossref{https://doi.org/10.1023/B:FAIA.0000034047.27498.51}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000224148100010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-3142683241}
Linking options:
  • https://www.mathnet.ru/eng/faa112
  • https://doi.org/10.4213/faa112
  • https://www.mathnet.ru/eng/faa/v38/i2/p91
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
    Statistics & downloads:
    Abstract page:445
    Full-text PDF :219
    References:74
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024