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, 2018, Volume 52, Issue 1, Pages 65–69
DOI: https://doi.org/10.4213/faa3454 (Mi faa3454) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

Invariant Subspaces for Commuting Operators on a Real Banach Space

V. I. Lomonosova, V. S. Shul'manb

a Department of Mathematics, Kent State University, Kent, USA
b Department of Higher Mathematics, Vologda State University, Vologda, Russia
Full-text PDF (131 kB) Citations (1)
References:
PDF
HTML
DOI: https://doi.org/10.4213/faa3454
Abstract: It is proved that the commutative algebra $\mathcal{A}$ of operators on a reflexive real Banach space has an invariant subspace if each operator $T\in\mathcal{A}$ satisfies the condition
$$ \|1-\varepsilon T^2\|_e\le 1+o(\varepsilon)\ \text{as}\ \varepsilon\searrow 0 $$
where $\|\cdot\|_e$ denotes the essential norm. This implies the existence of an invariant subspace for any commutative family of essentially self-adjoint operators on a real Hilbert space.
Keywords: Banach space, algebra of operators, invariant subspace.
Received: 09.11.2016
English version:
Functional Analysis and Its Applications, 2018, Volume 52, Issue 1, Pages 53–56
DOI: https://doi.org/10.1007/s10688-018-0207-6
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: V. I. Lomonosov, V. S. Shul'man, “Invariant Subspaces for Commuting Operators on a Real Banach Space”, Funktsional. Anal. i Prilozhen., 52:1 (2018), 65–69; Funct. Anal. Appl., 52:1 (2018), 53–56
Citation in format AMSBIB
\Bibitem{LomShu18}
\by V.~I.~Lomonosov, V.~S.~Shul'man
\paper Invariant Subspaces for Commuting Operators on a Real Banach Space
\jour Funktsional. Anal. i Prilozhen.
\yr 2018
\vol 52
\issue 1
\pages 65--69
\mathnet{http://mi.mathnet.ru/faa3454}
\crossref{https://doi.org/10.4213/faa3454}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3762288}
\elib{https://elibrary.ru/item.asp?id=32428044}
\transl
\jour Funct. Anal. Appl.
\yr 2018
\vol 52
\issue 1
\pages 53--56
\crossref{https://doi.org/10.1007/s10688-018-0207-6}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000428558200007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044770217}
Linking options:
  • https://www.mathnet.ru/eng/faa3454
  • https://doi.org/10.4213/faa3454
  • https://www.mathnet.ru/eng/faa/v52/i1/p65
    • 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
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
    Statistics & downloads:
    Abstract page:491
    Full-text PDF :63
    References:73
    First page:44
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024