一类无限算子代数的射影酉群的有界正规生成
Bounded normal generation for projective unitary groups of certain infinite operator algebras
摘要：
研究了Calkin代数的单位元的连通分支的射影酉群中，固定共轭类的乘积如何快速覆盖整个群，以及III型因子von Neumann代数的射影酉群.我们的结果是，所需的因子的数量是小到允许的（本质）运营商规范-在类比的结果Liebeck-Shalev为非阿贝尔有限单群和类似的结果酉群的II_1-因素。
英文摘要：
We study the question how quickly products of a fixed conjugacy class cover the entire group in the projective unitary group of the connected component of the identity of the Calkin algebra, as well as the projective unitary group of a factor von Neumann algebra of type III. Our result is that the number of factors that are needed is as small as permitted by the (essential) operator norm - in analogy to a result of Liebeck-Shalev for non-abelian finite simple groups and analogous results for unitary groups of II_1-factors.
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