Computation of antieigenvalues

μ1(T) measures the maximum turning capability of T . A vector f for which the inf in (1.1) is attained is called an antieigenvector of T . Cosine of T has important applications in pure operator theory as well as numerical analysis (see [3, 4, 6]). In [7, 8, 11], we have computed the first antieigenvalue of normal accretive operators in terms of eigenvalues of these operators. In [12], we computed the first antieigenvalue for certain classes of matrices on the real field. In this note, we will focus on computation and approximation of the first antieigenvalue of general accretive operators. Our work in this note is a generalization of our work in [7, 8, 11] to certain classes of nonnormal operators. We will start with the case of a general two-by-two matrix.