Some results on g-frames in Hilbert spaces

In this paper we show that every g-frame for a Hilbert space H can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. We also show that every g-frame can be written as a sum of two tight g-frames with g-frame bounds one or a sum of a g-orthonormal basis and a g-Riesz basis for H. We further give necessary and sufficient conditions on g-Bessel sequences {Λi element of L(H, Hi): i element of J} and {Γi element of L(H, Hi): i element of J} and operators L1 , L2 on H so that {ΛiL1 +ΓiL2 : i element of J} is a g-frame for H. We next show that a g-frame can be added to any of its canonical dual g-frame to yield a new g-frame.