Abstract
In this paper, we investigate the g-frame and Bessel g-sequence related to a linear bounded operator in Hilbert space, which we call a -g-frame and a -dual Bessel g-sequence, respectively. Since the frame operator for a -g-frame may not be invertible, there is no classical canonical dual for a -g-frame. So we characterize the concept of a canonical -dual Bessel g-sequence of a -g-frame that generalizes the classical dual of a g-frame. Moreover, we use a family of linear operators to characterize atomic systems. We also consider the construction of new atomic systems from given ones and bounded operators.
Citation
Dongwei Li. Jinsong Leng. Tingzhu Huang. "Generalized frames for operators associated with atomic systems." Banach J. Math. Anal. 12 (1) 206 - 221, January 2018. https://doi.org/10.1215/17358787-2017-0050
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