Induced sequences and weaving of g-frames

Abstract

In this paper we use the type I induced sequence $\{u_{ik}: i\in I, k\in K_i\}$ of a given
g-Bessel sequence $\{\Lambda_i:i\in I\}$ to characterize whether $\{\Lambda_i:i\in I\}$ are g-Riesz frames, near g-Riesz bases and near exact g-frames, and vice versa. We also characterize the precise relationship between the synthesis operators of a given g-Bessel sequence and its type II induced sequence. Finally, we discuss whether the sums $\Lambda+\Delta$ and $\Gamma+\Theta$ are woven, where $\{\Lambda_i: i\in I\}$ and $\{\Gamma_i: i\in I\}$ are woven and $\Delta,\Theta$ are g-Bessel sequences.