Research articles
ScienceAsia 45(2019): 285291 doi:
10.2306/scienceasia15131874.2019.45.285
Weaving of Kgframes in Hilbert spaces
XiangChun Xiao^{a,*}, GuoRong Zhou^{a}, YuCan Zhu^{b}
ABSTRACT: In this study, we mainly discuss the weaving of Kgframes in Hilbert spaces. Note that the concept
of weaving was recently proposed by Bemrose et al to solve a question in distributed signal processing. We give a
sufficient condition such that the left sequence can still be Kwoven in R(K) by deleting some elements from a Kwoven
pair of Kgframes. We then give three different types of perturbation conditions such that, under them, the Kgframes
{Λ_{j} : j ∈ J} and {Γ_{j} : j ∈ J} or the types {Λ_{j} T_{1}^{∗} : j ∈ J} and {Γ_{j} T_{2}^{∗} : j ∈ J} can be Kwoven in R(K), where T_{1}, T_{2} are
surjective operators on U .
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^{a} 
Department of Mathematics, Xiamen University of Technology, Xiamen 361024 China 
^{b} 
Department of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116 China 
* Corresponding author, Email: xxc570@163.com
Received 10 Jan 2019, Accepted 12 May 2019
