Recently, Gehér and Šemrl have characterized the general form of surjective isometries of the set of all projections on an infinite-dimensional separable Hilbert space using unitaries and antiunitaries. In this paper, we study the surjective L²-isometries of the projection lattice of an infinite dimensional Hilbert space and show that every such isometry can also be described by unitaries and antiunitaries.

中文翻译：

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投影格上的射影L 2-等距

最近，Gehér和Šemrl用characterized元和反rl元描述了无穷维可分离希尔伯特空间上所有投影集的射影等距的一般形式。在本文中，我们研究了无限维希尔伯特空间的投影格的射影L ^2-等距，并表明，每个这样的等距也可以用unit和反unit来描述。