  In this paper we show that every g-frame for an \linebreak infinite
dimensional Hilbert space $\mathcal{H}$ can be written as a sum of three
g-orthonormal bases for $\mathcal{H}$. Also, we prove that every g-frame can be
represented as a linear combination of two g-orthonormal bases if and only if
it is a g-Riesz basis. Further, we show each g-Bessel multiplier is a Bessel
multiplier and investigate the inversion of g-frame multipliers. Finally, we
introduce the concept of controlled g-frames and weighted g-frames and show
that the sequence induced by each controlled g-frame (resp. weighted g-frame)
is a controlled frame (resp. weighted frame).
