As a consequence of the main result of the paper we obtain that every 2-local isometry of the $C^*$-algebra $B(H)$ of all bounded linear operators on a separable infinite-dimensional Hilbert space $H$ is an isometry. We have a similar statement concerning the isometries of any extension of the algebra of all compact operators by a separable commutative $C^*$-algebra. Therefore, on those $C^*$-algebras the isometries are completely determined by their local actions on the two-point subsets of the underlying algebras.AMS 2000 Mathematics subject classification: Primary 47B49
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机译：作为本文主要结果的结果，我们获得了可分无穷维希尔伯特空间$ H $上所有有界线性算子的$ C ^ * $-代数$ B（H）$的每个2局部等距是等轴测图。对于所有紧算子的代数的任何等距性，我们都有一个类似的陈述，即可分离的交换C $ * $-代数。因此，在那些$ C ^ * $代数上，等式完全取决于它们对基础代数的两点子集的局部作用.AMS 2000数学主题分类：初级47B49
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