For a Banach space, the notion of a regular linear relation is introduced and studied. Also, the regular resolvent set for a closed linear relation is introduced and investigated. Certain characterizations of regular resolvents are obtained in terms of the gap metric between corresponding null spaces, and in terms of generalized resolvents of the linear relation itself, respectively.

中文翻译：

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Banach空间上的正则线性关系

对于 Banach 空间，引入并研究了正则线性关系的概念。此外，还介绍并研究了封闭线性关系的正则解算集。分别根据对应零空间之间的间隙度量和线性关系本身的广义解析来获得规则解析器的某些特征。