On the norm of a Schur product (Q1078288)

The author estimates the norm of the mapping \(X\mapsto A\circ X\) on \(M_ n({\mathbb{C}})\), where ''\(\circ ''\) is the Schur-Hadamard (coordinatewise) product of matrices, and X has the norm it acquires as a linear operator on a complex n-dimensional Hilbert space. Lower and upper bounds are obtained in terms of the matrix entries of A, \((A^*A)^{1/2}\) and \((AA^*)^{1/2}\).