In this article, the properties of completeness, being Riesz, being basis and minimality of a pair of g-sequences K ¼ fKi : H ! Higi2I and C ¼ fCi : H ! Higi2I 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 K. The effect of invertibility of the multiplier operator of sequences K; C on the above-mentioned properties will be investigated.
