Norm of Schur Multiplication for Schatten Norm
Copyright policy )Norm of Schur Multiplication for Schatten Norm
Let \(\| S_ A\|_ p\) denote the operator norm of the Hadamard- Schur multiplication operator, determined by a given matrix A, on the matrix algebra \(M_ n({\mathbb{C}})\) equipped with the Schatten p-norm. The author shows that \(p\mapsto \| S_ A\|_ p\) is a log-convex function of \(p^{-1}\), \(p\geq 1\), which is decreasing for \(1\leq p\leq 2\), and increasing for \(2\leq p<\infty\).
Linear transformations, semilinear transformations, Norms of matrices, numerical range, applications of functional analysis to matrix theory, log-convex function, matrix algebra, Hadamard-Schur multiplication operator, Schatten p-norm
Linear transformations, semilinear transformations, Norms of matrices, numerical range, applications of functional analysis to matrix theory, log-convex function, matrix algebra, Hadamard-Schur multiplication operator, Schatten p-norm
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