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Properties of bounded representations for $G$-frames (2005.04395v1)
Published 9 May 2020 in math.FA
Abstract: Due to the importance of frame representation by a bounded operator in dynamical sampling, researchers studied the frames of the form ${T{i-1} f}_{i\in \mathbb{N}}$, which $f$ belongs to separable Hilbert space $\mathcal{H}$ and $T\in B(\mathcal{H})$, and investigated the properties of $T$. Given that $g$-frames include the wide range of frames such as fusion frames, the main purpose of this paper is to study the characteristics of the operator $T$ for $g$-frames of the form ${\Lambda T{i-1} \in B(\mathcal{H},\mathcal{K}):i\in \mathbb{N}}$.