The Banach spaces associated with g-frames. (English) Zbl 1482.42080
The article under review addressed reconstructions, existence and dilations in the Banach spaces induced by a g-frame and \(l_p(\bigoplus_{i\in\mathbb N}\mathcal H_i)\) with \(1\le p\le 2\). The authors proved that for all closed subspaces of a Hilbert space \(\mathcal H\), only the finite dimensional ones with a g-orthonormal basis can be realized as such a Banach space associated g-frame, and that under some conditions of the g-frame, the g-frame expansion of any element in the Banach space associated with it converges in both the Hilbert space norm and the associated Banach norm. A dilation result was also obtained.
Reviewer: Yunzhang Li (Beijing)
MSC:
| 42C15 | General harmonic expansions, frames |
| 46L10 | General theory of von Neumann algebras |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
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