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Research articles

ScienceAsia 45 (2019): 285-291 |doi: 10.2306/scienceasia1513-1874.2019.45.285

Weaving of K-g-frames in Hilbert spaces

Xiang-Chun Xiaoa,*, Guo-Rong Zhoua, Yu-Can Zhub

ABSTRACT:     In this study, we mainly discuss the weaving of K-g-frames 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 K-woven in R(K) by deleting some elements from a K-woven pair of K-g-frames. We then give three different types of perturbation conditions such that, under them, the K-g-frames {Λj : jJ} and {Γj : jJ} or the types {Λj T1 : jJ} and {Γj T2 : jJ} can be K-woven in R(K), where T1, T2 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, E-mail: xxc570@163.com

Received 10 Jan 2019, Accepted 12 May 2019