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

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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.

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

Bibliographic databases:

UDC: 517.962

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} 

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Citing articles on Google Scholar: Russian citations, English citations
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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
2. Sedaev A.A., Sukochev F.A., “Dixmier Measurability in Marcinkiewicz Spaces and Applications”, J. Funct. Anal., 265:12 (2013), 3053–3066
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
4. Gayral V., Sukochev F., “Dixmier Traces and Extrapolation Description of Noncommutative Lorentz Spaces”, J. Funct. Anal., 266:10 (2014), 6256–6317
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