Generalized Weaving Frames for Operators in Hilbert Spaces

This paper studies weaving properties of a family of operators which are analysis and synthesis systems with frame-like properties for closed subspaces of a separable Hilbert space H, where the lower frame condition is controlled by a bounded operator on H. In short, this family of operators is called a Θ -g-frame, where Θ is a bounded operator on H. We present sufficient conditions for weaving Θ -g-frames in separable Hilbert spaces. A characterization of weaving Θ -g-frames in terms of an operator is given. It is shown that if frame bounds of frames associated with atomic spaces are positively confined, then Θ -g-woven frames gives ordinary weaving Θ -frames and vice-versa. We provide classes of operators for weaving Θ -g-frames.