Abstract
Let be a g-Bessel sequence of a Hilbert space. This study uses the type-II induced sequences
of
to characterize
to be a tight g-frame and a g-orthonormal basis. We also obtain the exact relationship between the synthesis operators of
and its type-II induced sequences. We then use the type-I induced sequences of
to characterize the (maximum) robustness to erasures and (maximum) uniform excess of
, and vice versa. Finally, we estimate the upper error bound of type-I induced sequences under some perturbations of
and
, and vice versa.
Disclosure statement
The authors declare that they have no conflict of interest.