During half a century, singular traces on ideals of Hilbert space operators have been constructed by looking for linear forms on associated sequence ideals. Only recently, the author was able to eliminate this auxiliary step by directly applying Banach’s version of the extension theorem; see (Integral Equ. Oper. Theory 91, 21, 2019 and 92, 7, 2020). Of course, the relationship between the new approach and the older ones must be investigated. In the first paper, this was done for $${\mathfrak {L}}_{1,\infty } (H)$$ L 1 , ∞ ( H ) . To save space, such considerations were postponed in the second paper, which deals with a large class of principal ideals, called simply generated. This omission will now be rectified.

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更多关于简单生成算子理想上的奇异迹

半个世纪以来，通过寻找相关序列理想上的线性形式，已经构建了希尔伯特空间算子理想上的奇异迹。直到最近，作者才能够通过直接应用 Banach 版本的扩展定理来消除这个辅助步骤；参见（Integral Equ. Oper. Theory 91, 21, 2019 和 92, 7, 2020）。当然，必须调查新方法和旧方法之间的关系。在第一篇论文中，这是针对 $${\mathfrak {L}}_{1,\infty } (H)$$ L 1 , ∞ ( H ) 完成的。为了节省篇幅，在第二篇论文中推迟了这些考虑，该论文涉及一大类主要理想，称为简单生成。现在将纠正这一遗漏。