Decompositions of \(g\)-frames and duals and pseudoduals of \(g\)-frames in Hilbert spaces (Q492517)

Summary: Firstly, we study the representation of \(g\)-frames in terms of linear combinations of simpler ones such as \(g\)-orthonormal bases, \(g\)-Riesz bases, and normalized tight \(g\)-frames. Then, we study the dual and pseudodual of \(g\)-frames, which are critical components in reconstructions. In particular, we characterize the dual \(g\)-frames in a constructive way; that is, the formulae for dual \(g\)-frames are given. We also give some \(g\)-frame like representations for pseudodual \(g\)-frame pairs. The operator parameterizations of \(g\)-frames and decompositions of bounded operators are the key tools to prove our main results.