RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. Vyssh. Uchebn. Zaved. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. Vyssh. Uchebn. Zaved. Mat., 2009, Number 12, Pages 90–94 (Mi ivm6030)  

This article is cited in 4 scientific papers (total in 4 papers)

Brief communications

Singular symmetric functionals and stabilizing subspaces of Marcinkiewicz spaces

A. A. Sedaev

Voronezh State University of Architecture and Civil Engineering, Voronezh, Russia

Abstract: We consider Marcinkiewicz spaces of functions measurable on a semiaxis that admit a wide set of singular symmetric Dixmier functionals. For elements of these spaces we study the measurability property introduced by A. Connes. We establish that this property is closely connected with the Tauberian property (which is more strong) but is not reduced to it. We specify the maximal subspace of the Marcinkiewicz space such that for its elements both properties are equivalent. We prove that this subspace is not reducible to other known subspaces of the Marcinkiewicz space and that it plays an important role in the theory of Dixmier functionals.

Keywords: singular Dixmier traces, singular symmetric functionals, Connes measurable elements.

Full text: PDF file (161 kB)
References: PDF file   HTML file

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:12, 77–80

Bibliographic databases:

UDC: 517.962
Received: 14.05.2009

Citation: A. A. Sedaev, “Singular symmetric functionals and stabilizing subspaces of Marcinkiewicz spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 12, 90–94; Russian Math. (Iz. VUZ), 53:12 (2009), 77–80

Citation in format AMSBIB
\Bibitem{Sed09}
\by A.~A.~Sedaev
\paper Singular symmetric functionals and stabilizing subspaces of Marcinkiewicz spaces
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 12
\pages 90--94
\mathnet{http://mi.mathnet.ru/ivm6030}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2664478}
\zmath{https://zbmath.org/?q=an:1189.46023}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 12
\pages 77--80
\crossref{https://doi.org/10.3103/S1066369X09120123}


Linking options:
  • http://mi.mathnet.ru/eng/ivm6030
  • http://mi.mathnet.ru/eng/ivm/y2009/i12/p90

    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. Carey A., Sukochev F., “Measurable Operators and the Asymptotics of Heat Kernels and Zeta Functions”, J. Funct. Anal., 262:10 (2012), 4582–4599  crossref  mathscinet  zmath  isi  elib
    2. Sedaev A.A., Sukochev F.A., “Dixmier Measurability in Marcinkiewicz Spaces and Applications”, J. Funct. Anal., 265:12 (2013), 3053–3066  crossref  mathscinet  zmath  isi  elib
    3. Sukochev F., Usachev A., Zanin D., “Generalized Limits with Additional Invariance Properties and their Applications to Noncommutative Geometry”, Adv. Math., 239 (2013), 164–189  crossref  mathscinet  zmath  isi  elib
    4. Gayral V., Sukochev F., “Dixmier Traces and Extrapolation Description of Noncommutative Lorentz Spaces”, J. Funct. Anal., 266:10 (2014), 6256–6317  crossref  mathscinet  zmath  isi  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
    Number of views:
    This page:230
    Full text:55
    References:20
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020