Joint Similarities and Parameterizations for Dilations of Dual g -frame Pairs in Hilbert Spaces |
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Authors: | Xun Xiang Guo |
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Affiliation: | Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, P. R. China |
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Abstract: | In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular, for the dilations of a given pair of dual g-frames, we introduce the concept of joint complementary g-frames and prove that the joint complementary g-frames of a pair of dual g-frames are unique in the sense of joint similarity, which then helps to obtain a sufficient condition such that the complementary g-frames of a g-frame are unique in the sense of similarity and show that the set of dilations of a given dual g-frame pair are parameterized by a set of invertible diagonal operators. For the dilations of pairs of dual g-frames, we prove that the set of dilations of pairs of dual g-frames are parameterized by a set of invertible upper triangular operators. |
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Keywords: | g-frame dual g-frame pair dilation g-Riesz basis joint similarity |
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