On characterization and construction of bi-g-frames. (English) Zbl 07832006
Summary: 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.
MSC:
| 47A58 | Linear operator approximation theory |
| 42C15 | General harmonic expansions, frames |
| 47B90 | Operator theory and harmonic analysis |
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