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On the geometry of von Neumann algebra preduals
http://hdl.handle.net/2237/00030630
http://hdl.handle.net/2237/00030630ee8d5411-fe17-4408-9dcb-f8f156e0ce4d
名前 / ファイル | ライセンス | アクション |
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1209_3391 (186.3 kB)
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Item type | 学術雑誌論文 / Journal Article(1) | |||||
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公開日 | 2019-08-28 | |||||
タイトル | ||||||
タイトル | On the geometry of von Neumann algebra preduals | |||||
言語 | en | |||||
著者 |
Martín, Miguel
× Martín, Miguel× Ueda, Yoshimichi |
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アクセス権 | ||||||
アクセス権 | open access | |||||
アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||
権利 | ||||||
言語 | en | |||||
権利情報 | “This is a post-peer-review, pre-copyedit version of an article published in [Positivity]. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11117-013-0259-z”. | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | von Neumann algebra | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Predual | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Factor | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Diffuseness | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Daugavet property | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Extreme point | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Girth curve | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Flat space | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Ultraproduct | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Ultrapower | |||||
抄録 | ||||||
内容記述 | Let M be a von Neumann algebra and let M⋆ be its (unique) predual. We study when for every φ∈M⋆ there exists ψ∈M⋆ solving the equation ∥φ±ψ∥=∥φ∥=∥ψ∥. This is the case when M does not contain type I nor type III1 factors as direct summands and it is false at least for the unique hyperfinite type III1 factor. We also characterize this property in terms of the existence of centrally symmetric curves in the unit sphere of M⋆ of length 4. An approximate result valid for all diffuse von Neumann algebras allows to show that the equation has solution for every element in the ultraproduct of preduals of diffuse von Neumann algebras and, in particular, the dual von Neumann algebra of such ultraproduct is diffuse. This shows that the Daugavet property and the uniform Daugavet property are equivalent for preduals of von Neumann algebras. | |||||
言語 | en | |||||
内容記述タイプ | Abstract | |||||
出版者 | ||||||
言語 | en | |||||
出版者 | Springer | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプresource | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
出版タイプ | ||||||
出版タイプ | AM | |||||
出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||
DOI | ||||||
関連タイプ | isVersionOf | |||||
識別子タイプ | DOI | |||||
関連識別子 | https://doi.org/10.1007/s11117-013-0259-z | |||||
ISSN(print) | ||||||
収録物識別子タイプ | PISSN | |||||
収録物識別子 | 1385-1292 | |||||
書誌情報 |
Positivity 巻 18, 号 3, p. 519-530, 発行日 2014-09 |
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著者版フラグ | ||||||
値 | author |