We prove that for normal operators N₁, \({N_2} \in {\cal L}({\cal H})\), the generalized commutator [N₁, N₂; X] approaches zero when [N₁, N₂; [N₁, N₂; X]] tends to zero in the norm of the Schatten-von Neumann class \({{\cal C}_p}\) with p > 1 and X varies in a bounded set of such a class.

中文翻译：

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关于Kleinecke-Shirokov定理

我们证明，对于正规算子N ₁，\（{N_2} \ in {\ cal L}（{\ cal H}）\），广义交换子[ N ₁，N ₂ ; X ]接近零当[ Ñ ₁，Ñ ₂ ; [ N ₁，N ₂ ; X ]在上Schatten-冯·诺依曼类的范数趋于零\（{{\ CALÇ} _p} \）与p > 1和X在某个有界集这样一类的不同而不同。