Tight K-frames and weaving of K-frames

Abstract

In this paper we find that a result of an equivalent characterization of tight K-g-frames obtained by Huang and Shi is incorrect, and we give a sufficient condition for a given Bessel sequence to be a tight K-frame. We also characterize the weaving of K-frames in Hilbert spaces. We give several kinds of sufficient conditions such that the type $\{T_{1} f_{i}\}_{i\in I}$ and $\{T_{2} g_{i}\}_{i\in I}$ are K-woven (resp. woven) on $\mathcal {H}$ or its subspace R(K), given that $\{f_{i}\}_{i\in I}$ and $\{g_{i}\}_{i\in I}$ are K-frames (resp. frames) on $\mathcal {H}$ and $T_{1}, T_{2}$ are surjective operators on $\mathcal {H}$. Finally we discuss that we can plus two different Bessel sequences to a K-woven pair such that the new obtained pair are K-woven on $\mathcal {H}$.