Cartesian decomposition of matrices and some norm inequalities
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Abstract:
Let X be an n-square complex matrix with the Cartesian decomposition X = A + i B, where A and B are n times n Hermitian matrices. It is known that $Vert X Vert_p^2 leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)$, where $p geq 2$ and $Vert . Vert_p$ is the Schatten p-norm. In this paper, this inequality and some of its improvements are studied and investigated for the joint C-numerical radius, joint spectral radius, and for the C-spectral norm of matrices.
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Journal title
volume 3 issue 2
pages 33- 42
publication date 2016-12-01
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