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dc.contributor.authorBlecher, David P.
dc.contributor.authorLabuschagne, Louis
dc.date.accessioned2018-10-29T12:59:58Z
dc.date.available2018-10-29T12:59:58Z
dc.date.issued2018
dc.identifier.citationBlecher, D.P. & Labuschagne, L. 2018. Ueda’s peak set theorem for general Von Neumann algebras. Transactions of the American Mathematical Society, 370(11):8215-8236. [https://doi.org/10.1090/tran/7275]en_US
dc.identifier.issn0002-9947
dc.identifier.issn1088-6850 (Online)
dc.identifier.urihttp://hdl.handle.net/10394/31573
dc.identifier.urihttps://doi.org/10.1090/tran/7275
dc.identifier.urihttp://www.ams.org/journals/tran/2018-370-11/S0002-9947-2018-07275-0/S0002-9947-2018-07275-0.pdf
dc.description.abstractWe extend Ueda’s peak set theorem for subdiagonal subalgebras of tracial finite von Neumann algebras to σ-finite von Neumann algebras (that is, von Neumann algebras with a faithful state, which includes those on a separable Hilbert space or with separable predual). To achieve this extension, completely new strategies had to be invented at certain key points, ultimately resulting in a more operator algebraic proof of the result. Ueda showed in the case of finite von Neumann algebras that his peak set theorem is the fountainhead of many other very elegant results, like the uniqueness of the predual of such subalgebras, a highly refined F & M Riesz type theorem, and a Gleason-Whitney theorem. The same is true in our more general setting, and indeed we obtain a quite strong variant of the last mentioned theorem. We also show that set theoretic issues dash hopes for extending the theorem to some other large general classes of von Neumann algebras, for example finite or semi-finite ones. Indeed certain cases of Ueda’s peak set theorem for a von Neumann algebra M may be seen as ‘set theoretic statements’ about M that require the sets to not be ‘too large’en_US
dc.language.isoenen_US
dc.publisherAMSen_US
dc.subjectSubdiagonal operator algebraen_US
dc.subjectPeak projectionen_US
dc.subjectNoncommutative Lebesgue decompositionen_US
dc.subjectNoncommutative Hardy spaceen_US
dc.subjectSigma-finite Von Neumann algebraen_US
dc.subjectKaplansky density theoremen_US
dc.subjectF & M Riesz theoremen_US
dc.titleUeda’s peak set theorem for general Von Neumann algebrasen_US
dc.typeArticleen_US
dc.contributor.researchID22982477 - Labuschagne, Louis Ernst


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