Let $\mathcal{L}(H)$ be the space of linear operators acting from the finite-dimensional real Hilbert space into itself. The purpose of this paper is to present results concerning the geometric properties of some subspaces of $\mathcal{L}(H)$. In particular, vertices of the closed unit ball of those subspaces are discussed. The problem of best approximation in the space $\mathcal{L}(l_2^2)$ is investigated. Moreover, in this paper we show an example of an effective method seeking a unique minimal projection which is strongly unique.

中文翻译：

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L(H) 中子空间单位球的顶点和 L(l22) 中最佳近似的强唯一性

让 $\mathcal{升}(H)$是从有限维实 Hilbert 空间作用到自身的线性算子的空间。本文的目的是展示关于一些子空间的几何性质的结果$\mathcal{升}(H)$. 特别地，讨论了这些子空间的封闭单位球的顶点。空间中的最佳逼近问题$\mathcal{升}({升}_2^2)$被调查。此外，在本文中，我们展示了一个有效方法的例子，该方法寻求一个非常独特的独特最小投影。