Triangular truncation and finding the norm of a Hadamard multiplier (Q1190121)

Let \(K_ n\) be the norm of the operator on \(M_ n(\mathbb{C})\) which assigns to each matrix its lower triangular part (including the diagonal). The authors show that \(\lim_{n\to\infty}(K_ n/\log n)=1/\pi\). The values of \(K_ 2\), \(K_ 3\), and \(K_ 4\) are calculated explicitly. (The matrix algebra \(M_ n(\mathbb{C})\) is equipped with the operator norm derived from the scalar product on \(\mathbb{C}^ n\)).