We show that a bounded linear operator A ∈ B(H) is a multiple of a unitary operator if and only if AZ and ZA always have the same numerical radius or the same numerical range for all (rank one) Z ∈ B(H). More generally, for any bounded linear operators A,B ∈ B(H), we show that AZ and ZB always have the same numerical radius (resp., the same numerical range) for all (rank one) Z ∈ B(H) if and on...

We characterize those linear operators on triangular or diagonal matrices preserving the numerical range or radius.

We characterize those linear operators on triangular or diagonal matrices preserving the numerical range or radius.

The current two main methods for computing the numerical are level-set approach of Mengi and Overton cutting-plane method Uhlig, but until now, no formal convergence rate results have been established either. In practice, which is faster also unclear, with Uhlig's sometimes being much than Overton's approach, on other problems, slower. this paper, we clarify issue propose three improved methods...