On characterization and construction of bi-g-frames

Bi-g-frame, was introduced as a pair of operator sequences, could obtain a new reconstruction formula for elements in Hilbert spaces. In this paper we aim at studying the characterizations and constructions of bi-g-frames. For a bi-g-frame \((\Lambda ,\,\Gamma )\), the relationship between the sequence \(\Lambda \) and the sequence \(\Gamma \) is very crucial, we are devoted to characterizing bi-g-frames, whose component the sequences are g-Bessel sequences, g-frames and so on. Then we discuss the construction of new bi-g-frames, we show that bi-g-frames can be constructed by specific operators, dual g-frames and g-dual frames. Especially, we also study those bi-g-frames for which one of the constituent sequences is a g-orthonormal basis.