Abstract
In this paper, we investigate weaving frames in Hilbert C ∗ -modules. We show that the equivalence of woven and weakly woven frames is still true for modular frames under certain conditions. By using the analysis operators of frames and frame operators of canonical duals, we obtain several perturbation results for given weaving frames and different weaving frame pairs. When the C ∗ -algebra is nonunital, we derive a correspondence of adjointable operators which is bounded below woven families. Finally, we discuss the redundancy of weaving frames in Hilbert C ∗ -modules.
Highlights
Due to the useful applications in the characterization of function spaces, signal processing, and many other fields of applications, the theory of frames has developed rather rapidly in recent years
Two frames xjj∈J and yjj∈J are said to be woven if there exist constants 0 < C ≤ D such that, for every subset σ ⊂ J (J is a finite or countable index set), the family xjj∈σ ∪ yjj∈σc is a frame with frame bounds (C, D)
We investigate the weaving properties of modular fames
Summary
Due to the useful applications in the characterization of function spaces, signal processing, and many other fields of applications, the theory of frames has developed rather rapidly in recent years. By allowing the inner product to take values in a C∗-algebra, Hilbert C∗-modules are natural generalizations of Hilbert spaces. Not all bounded linear operators on Hilbert C∗-modules are adjointable. Us, there are many essential differences between Hilbert space frames and modular frames. We investigate the weaving properties of modular fames.
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