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Izvestiya: Mathematics, 2003, Volume 67, Issue 6, Pages 1187–1212
DOI: https://doi.org/10.1070/IM2003v067n06ABEH000461
(Mi im461)
 

This article is cited in 43 scientific papers (total in 43 papers)

Singular symmetric functionals and Banach limits with additional invariance properties

P. G. Dodds, B. de Pagter, A. A. Sedaev, E. M. Semenov, F. A. Sukochev
References:
Abstract: For symmetric spaces of measurable functions on the real half-line, we study the problem of existence of positive linear functionals monotone with respect to the Hardy–Littlewood semi-ordering, the so-called symmetric functionals. Two new wide classes of symmetric spaces are constructed which are distinct from Marcinkiewicz spaces and for which the set of symmetric functionals is non-empty. We consider a new construction of singular symmetric functionals based on the translation-invariance of Banach limits defined on the space of bounded sequences. We prove the existence of Banach limits invariant under the action of the Hardy operator and all dilation operators. This result is used to establish the stability of the new construction of singular symmetric functionals for an important class of generating sequences.
Received: 11.10.2002
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2003, Volume 67, Issue 6, Pages 111–136
DOI: https://doi.org/10.4213/im461
Bibliographic databases:
UDC: 517.51
Language: English
Original paper language: Russian
Citation: P. G. Dodds, B. De Pagter, A. A. Sedaev, E. M. Semenov, F. A. Sukochev, “Singular symmetric functionals and Banach limits with additional invariance properties”, Izv. RAN. Ser. Mat., 67:6 (2003), 111–136; Izv. Math., 67:6 (2003), 1187–1212
Citation in format AMSBIB
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\by P.~G.~Dodds, B.~De Pagter, A.~A.~Sedaev, E.~M.~Semenov, F.~A.~Sukochev
\paper Singular symmetric functionals and Banach limits with additional invariance properties
\jour Izv. RAN. Ser. Mat.
\yr 2003
\vol 67
\issue 6
\pages 111--136
\mathnet{http://mi.mathnet.ru/im461}
\crossref{https://doi.org/10.4213/im461}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2032092}
\zmath{https://zbmath.org/?q=an:1075.46028}
\transl
\jour Izv. Math.
\yr 2003
\vol 67
\issue 6
\pages 1187--1212
\crossref{https://doi.org/10.1070/IM2003v067n06ABEH000461}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-18844377723}
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  • https://doi.org/10.1070/IM2003v067n06ABEH000461
  • https://www.mathnet.ru/eng/im/v67/i6/p111
  • This publication is cited in the following 43 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:708
    Russian version PDF:329
    English version PDF:22
    References:77
    First page:1
     
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