We present direct and self-contained proofs of the existence of singular traces on sufficiently large classes of operator ideals that live on the separable infinite-dimensional real Hilbert space. Our only tool is Banach’s version of the extension theorem of linear forms. Thanks to the use of dyadic representations of operators, all proofs have become straightforward.

中文翻译：

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简单生成算子理想上奇异迹的存在

我们提出了关于存在于可分离的无限维实 Hilbert 空间上的足够大的算子理想类上奇异迹存在的直接和独立的证明。我们唯一的工具是 Banach 版本的线性形式的扩展定理。由于使用了运算符的二元表示，所有的证明都变得简单明了。