RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2011, Volume 89, Issue 4, Pages 547–557 (Mi mz7699)  

This article is cited in 3 scientific papers (total in 3 papers)

Universal Spaces of Subdifferentials of Sublinear Operators Ranging in the Cone of Bounded Lower Semicontinuous Functions

Yu. E. Linke

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: We study Fréchet's problem of the universal space for the subdifferentials $\partial P$ of continuous sublinear operators $P\colon V\to BC(X)_{\sim}$ which are defined on separable Banach spaces $V$ and range in the cone $BC(X)_\sim$ of bounded lower semicontinuous functions on a normal topological space $X$. We prove that the space of linear compact operators $L^{\mathrm c}(\ell^2,C(\beta X))$ is universal in the topology of simple convergence. Here $\ell^2$ is a separable Hilbert space, and $\beta X$ is the Stone–Ĉech compactification of $X$. We show that the images of subdifferentials are also subdifferentials of sublinear operators.

Keywords: sublinear operator, subdifferential, topology of simple convergence, lower semicontinuous function, Fréchet problem for universal spaces, separable Banach space, continuous selection

DOI: https://doi.org/10.4213/mzm7699

Full text: PDF file (476 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2011, 89:4, 519–527

Bibliographic databases:

UDC: 517.982+517.988
Received: 24.12.2008
Revised: 18.11.2010

Citation: Yu. E. Linke, “Universal Spaces of Subdifferentials of Sublinear Operators Ranging in the Cone of Bounded Lower Semicontinuous Functions”, Mat. Zametki, 89:4 (2011), 547–557; Math. Notes, 89:4 (2011), 519–527

Citation in format AMSBIB
\Bibitem{Lin11}
\by Yu.~E.~Linke
\paper Universal Spaces of Subdifferentials of Sublinear Operators Ranging in the Cone of Bounded Lower Semicontinuous Functions
\jour Mat. Zametki
\yr 2011
\vol 89
\issue 4
\pages 547--557
\mathnet{http://mi.mathnet.ru/mz7699}
\crossref{https://doi.org/10.4213/mzm7699}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2856746}
\transl
\jour Math. Notes
\yr 2011
\vol 89
\issue 4
\pages 519--527
\crossref{https://doi.org/10.1134/S0001434611030230}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000290038700023}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79955597728}


Linking options:
  • http://mi.mathnet.ru/eng/mz7699
  • https://doi.org/10.4213/mzm7699
  • http://mi.mathnet.ru/eng/mz/v89/i4/p547

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. V. Orlov, Z. I. Khalilova, “Compact subdifferentials in Banach spaces and their applications to variational functionals”, Journal of Mathematical Sciences, 211:4 (2015), 542–578  mathnet  crossref
    2. I. V. Orlov, “Introduction to sublinear analysis”, Journal of Mathematical Sciences, 218:4 (2016), 430–502  mathnet  crossref
    3. I. V. Orlov, S. I. Smirnova, “Invertibility of multivalued sublinear operators”, Eurasian Math. J., 6:4 (2015), 44–58  mathnet
  • Математические заметки Mathematical Notes
    Number of views:
    This page:296
    Full text:61
    References:26
    First page:6

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019