Sarason approach to optimal, 2-block and 4-block H^∞ norm

This paper introduces a new method for computating optimal 2-block and 4-block H^∞ norms. It is shown that the spectral radii of 2-block and 4-block operators can be found by calculating the largest singular value of a finite dimensional matrix formed from the matrix representation of the Sarason operator. This novel approach reveals the intimate relations among the Hankel, Toeplitz and Sarason operators and provides an efficient way for computing optimal H^∞ norms.