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Singular value and unitarily invariant norm inequalities for matrices
In this paper, we prove some new singular value and unitarily invariant norm inequalities for matrices. Among other results, it is shown that if X , Y ,...
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A Unitarily Invariant Norm Inequality for Positive Semidefinite Matrices and a Question of Bourin
In this article, we obtain a new unitarily invariant norm inequality for positive semidefinite matrices. In fact, we prove that if A and B are...
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Further unitarily invariant norm inequalities for positive semidefinite matrices
In this paper, we prove further unitarily invariant norm inequalities for positive semidefinite matrices. These inequalities generalize earlier...
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Unitarily invariant norms on finite von Neumann algebras
We give a characterization of all the unitarily invariant norms on a finite von Neumann algebra acting on a separable Hilbert space. The...
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Non-Linear Traces on Matrix Algebras, Majorization, Unitarily Invariant Norms and 2-Positivity
We study non-linear traces of Choquet type and Sugeno type on matrix algebras. They have certain partial additivities. We show that these partial...
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Inequalities of singular values and unitarily invariant norms for sums and products of matrices
In this work, we investigate inequalities of singular values and unitarily invariant norms for sums and products of matrices. First, we prove that
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Unitarily invariant norm inequalities for matrix means
The main target of this article is to present several unitarily invariant norm inequalities which are refinements of arithmetic-geometric mean, Heinz...
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Singular value and unitarily invariant norm inequalities for sums and products of operators
In this note, we mainly investigate singular value and unitarily invariant norm inequalities for sums and products of operators. First, we present...
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New Hilbert–Schmidt norm inequalities for positive semidefinite matrices
Let A and B be positive semidefinite matrices, and let X be any matrix. As a generalization of an earlier Hilbert–Schmidt norm inequality, we prove...
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Singular value and norm inequalities for products and sums of matrices
In this paper, we give singular value and norm inequalities involving convex functions of positive semidefinite matrices. Our results generalize some...
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A Note on the Invariant Subspace Problem
The invariant subspace problem asks whether every bounded linear operator on a separable complex Hilbert space has a nontrivial invariant subspace....
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Log-majorization and matrix norm inequalities with application to quantum information
We are concerned with log-majorization for matrices in connection with the multivariate Golden–Thompson trace inequality and the Karcher mean (i.e.,...
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Uniqueness in Nuclear Norm Minimization: Flatness of the Nuclear Norm Sphere and Simultaneous Polarization
In this paper, we establish necessary and sufficient conditions for the existence of line segments (or flats ) in the sphere of the nuclear norm via...
