CONSTRUCTIONS OF WEAVING CONTINUOUS G-FRAMES for operators IN HILBERT SPACES

Weaving Continuous Controlled K-g-Gusion Frames in Hilbert Spaces

“…Woven frame is a new notion in frame theory which has been introduced by Bemrose et al [7]. Two frames {f i } i∈I and {g i } i∈I for H are called woven if there exist constants 0 < A ≤ B < +∞ such that for any subset σ ⊂ I the family {f i } i∈σ ∪ {g i } i∈σ c is a frame for H. This frame has been generalized for the discrete as well as the continuous case such as woven fusion frame [17], woven g-frame [24], woven g-fusion frame [25], woven K-g-fusion frame [32], continuous weaving frame [36], continuous weaving fusion frame [33], continuous weaving g-frames [3], weaving continuous K-g-frames [5], controlled weaving frames [29], continuous controlled K-gframes [30] etc. In this paper, woven continuous controlled K-g-fusion frame in Hilbert spaces is presented and some of their properties are going to be established.…”