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More accurate Young, Heinz, and Hölder inequalities for matrices

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Abstract

In this paper we deal with a more precise estimates for the matrix versions of Young, Heinz, and Hölder inequalities. First we give an improvement of the matrix Heinz inequality for the case of the Hilbert–Schmidt norm. Then, we refine matrix Young-type inequalities for the case of Hilbert–Schmidt norm, which hold under certain assumptions on positive semidefinite matrices appearing therein. Finally, we give the refinement and the reverse of the matrix Hölder inequality which holds for every unitarily invariant norm. As applications, we also obtain improvements of some well-known matrix inequalities in a quotient form. Our results are compared with the previously known from the literature.

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000, Zagreb, Croatia

    Mario Krnić

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  1. Mario Krnić
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Correspondence to Mario Krnić.

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Krnić, M. More accurate Young, Heinz, and Hölder inequalities for matrices. Period Math Hung 71, 78–91 (2015). https://doi.org/10.1007/s10998-015-0086-z

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  • DOI: https://doi.org/10.1007/s10998-015-0086-z

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