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Duality Mapping for Schatten Matrix Norms
2021
Numerical Functional Analysis and Optimization
In this paper, we fully characterize the duality mapping over the space of matrices that are equipped with Schatten norms. Our approach is based on the analysis of the saturation of the H€ older inequality for Schatten norms. We prove in our main result that, for p 2 ð1, 1Þ, the duality mapping over the space of real-valued matrices with Schatten-p norm is a continuous and single-valued function and provide an explicit form for its computation. For the special case p ¼ 1, the mapping is
doi:10.1080/01630563.2021.1922438
fatcat:qqvogpjpv5apvcrxtyecjcgxwi