Recently, duality principles in g-frame theory were studied. This paper addresses a relaxation of g-R-duals. We introduce the notion of weak g-R-dual in g-frame theory setting, and present the link between frame properties of a bounded operator sequence and its weak g-R-duals. Using weak g-R-duals, we characterize g-frames and (unitary) equivalence between g-frames. And using pseudo-inverse operators, we represent the canonical duals of weak g-R-duals. Some examples are also provided.

中文翻译：

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与弱 gR-对偶相关的对偶关系

最近，研究了g框架理论中的对偶原理。本文解决了g -R-对偶的松弛问题。我们在g框架理论设置中引入了弱g -R-对偶的概念，并展示了有界算子序列的框架属性与其弱g -R-对偶之间的联系。使用弱g -R-对偶，我们描述了g -frames 和g -frames 之间的（酉）等价性。并使用伪逆运算符，我们表示弱g -R-对偶的规范对偶。还提供了一些示例。