Characterizations and redundancies of g-frames in Hilbert spaces

Let{lambda(j):j is an element of J}be a g-Bessel sequence of a Hilbert space. Thisstudy uses the type-II induced sequences{lambda(jk)lambda j:j is an element of J,k is an element of K-j}of{lambda(j):j is an element of J}to characterize{lambda(j):j is an element of J}to be a tight g-frame anda g-orthonormal basis. We also obtain the exact relationship between the synthesis operators of{lambda(j):j is an element of J}and its type-II induced sequences. We then use the type-I induced sequences of{lambda(j):j is an element of J}to characterize the (maximum) robustness to erasures and (maxi-mum) uniform excess of{lambda(j:)j is an element of J}, and vice versa. Finally, we esti-matetheuppererrorboundoftype-Iinducedsequencesundersomeperturbations of{lambda(j):j is an element of J} and {gamma(j):j is an element of J}, and vice versa.