On the geometry of von Neumann algebra preduals
On the geometry of von Neumann algebra preduals
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论冯·诺依曼代数预变量的几何
DOI：
10.1007/s11117-013-0259-z
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发表时间：
2014
期刊：
影响因子：
1
通讯作者：
Yoshimichi Ueda
中科院分区：
文献类型：
--
作者：
Miguel Martin;Yoshimichi Ueda
设一个von Neumann代数，并设它的(唯一)准数。我们研究什么时候每个人都有解这个方程的机会。这是不包含I型和III型因子作为直接总和的情况，至少对于唯一的超有限III型因子是错误的。我们还通过在单位长度的球面上存在中心对称曲线来刻画这一性质。一个对所有扩散von Neumann代数有效的近似结果表明，该方程对扩散von Neumann代数的乘积的每一个元素都有解，特别地，这种超积的对偶von Neumann代数是扩散的.这表明，对于von Neumann代数的乘积，Dugavet性质和一致Dugavet性质是等价的。
Letbe a von Neumann algebra and letbe its (unique) predual. We study when for everythere existssolving the equation. This is the case whendoes not contain type I nor type IIIfactors as direct summands and it is false at least for the unique hyperfinite type IIIfactor. We also characterize this property in terms of the existence of centrally symmetric curves in the unit sphere ofof length. 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.