In a recent work (2016), the first author proved the fuzzy sum rule for the V-proximal subdifferential under some natural assumptions on an equivalent norm of the Banach spaces. In the present paper, we are going to prove that the class of Banach spaces satisfying the fuzzy sum rule is very large and contains all spaces as well as the sequence spaces , the Sobolev spaces , and the Schatten trace ideals .

中文翻译：

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-近可信赖Banach空间

在最近的工作（2016年）中，第一作者证明了在一些自然假设下，在等价的Banach空间范数下，V极限次微分的模糊和规则。在本文中，我们将证明满足模糊和规则的Banach空间类别非常大，并且包含所有空间 以及序列空间 ， Sobolev空间，以及Schatten追寻理想。