Continuous controlled K-g-frames 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.…”

Controlled Continuous∗-K-g-Frames for HilbertC∗-Modules

“…The concept of frames in Hilbert spaces has been introduced by Duffin and Schaeffer [1] in 1952 to study some deep problems in nonharmonic Fourier series. After the fundamental paper [2] by Daubechies et al, frame theory began to be widely used, particularly in the more specialized context of wavelet frame and Gabor frame [3,4]. Frames have been used in signal processing, image processing, data compression, and sampling theory.…”