Abstract
In this paper, we mainly parameterize $g$-frames in Hilbert space in terms of operators. Firstly, under the condition that there exists a $g$-orthonormal basis we establish the one to one correspondence between different kinds of $g$-frames with certain kinds of operators. Then we parameterize $g$-frames without the above restriction. Finally, we consider some special $g$-frames, and their operator parameterizations are established. We also obtain some interesting results on $g$-bases and $g$-dual frames of the transforms by applying the operator parameterizations of $g$-frames.
Citation
Xunxiang Guo. "OPERATOR PARAMETERIZATIONS OF $g$-FRAMES." Taiwanese J. Math. 18 (1) 313 - 328, 2014. https://doi.org/10.11650/tjm.18.2014.3264
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