Inequalities relating unitarily invariant norms and the numerical radius
Charles R. Johnson, Chi-Kwong Li · Linear and Multilinear Algebra · 1988
For a unitarily invariant norm N(⋅) and the numerical radius r(⋅) on , we determine the largest constant Cm and the smallest constant CM such that . Specialization to the p,k-norms includes the case in which N(⋅) is the Frobenius norm, which motivated this work. In addition, the nonzero matrices A for which equality is attained (in one of the above inequalities) are characterized.