Izv. Vyssh. Uchebn. Zaved. Mat., 2009, Number 12, Pages 90–94
This article is cited in 4 scientific papers (total in 4 papers)
Singular symmetric functionals and stabilizing subspaces of Marcinkiewicz spaces
A. A. Sedaev
Voronezh State University of Architecture and Civil Engineering, Voronezh, Russia
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.
singular Dixmier traces, singular symmetric functionals, Connes measurable elements.
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Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:12, 77–80
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
\paper Singular symmetric functionals and stabilizing subspaces of Marcinkiewicz spaces
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\jour Russian Math. (Iz. VUZ)
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Sedaev A.A., Sukochev F.A., “Dixmier Measurability in Marcinkiewicz Spaces and Applications”, J. Funct. Anal., 265:12 (2013), 3053–3066
Sukochev F., Usachev A., Zanin D., “Generalized Limits with Additional Invariance Properties and their Applications to Noncommutative Geometry”, Adv. Math., 239 (2013), 164–189
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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