In this article, the properties of completeness, being Riesz, being basis and minimality of a pair of g-sequences \(\Lambda =\{\Lambda _i :\mathcal {H}\longrightarrow \mathcal {H}_i\}_{i \in {\mathbb {I}}}\) and \(\Gamma =\{\Gamma _i :\mathcal {H}\longrightarrow \mathcal {H}_i\}_{i \in {\mathbb {I}}}\) are simultaneously studied as well as investigating the above-mentioned properties about the sequences of subspaces induced by them. We show that the above properties are an extension of the definitions known about a single g-sequence \(\Lambda\). The effect of invertibility of the multiplier operator of sequences \(\Lambda ,\Gamma\) on the above-mentioned properties will be investigated.

在本文中，完整性的性质，是 Riesz，是一对g序列的基和极小性\(\Lambda =\{\Lambda _i :\mathcal {H}\longrightarrow \mathcal {H}_i\}_ {i \in {\mathbb {I}}}\)和\(\Gamma =\{\Gamma _i :\mathcal {H}\longrightarrow \mathcal {H}_i\}_{i \in {\mathbb { I}}}\)被同时研究并研究了上述关于由它们诱导的子空间序列的属性。我们表明，上述属性是关于单个g序列\(\Lambda\)的已知定义的扩展。序列乘子算子可逆性的影响\(\Lambda ,\Gamma\)将研究上述特性。