Here, we show the equivalent conditions for integrability and being almost everywhere zero of trace-class operator-valued functions with respect to some spectral measure. Furthermore, we investigate the relation between the convergence of these functions and the one of their integrals.

中文翻译：

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跟踪类运算符值函数的E可集成性

在这里，我们显示了可积性的等效条件，并且相对于某些频谱测度，跟踪类算子值函数的各处几乎为零。此外，我们研究了这些函数的收敛与其积分之一之间的关系。