Elementary proofs of two theorems involving arguments of eigenvalues of a product of two unitary matrices
H. F. Chau, Yan Ting Lam · Journal of Inequalities and Applications · 2011
We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices--one by Childs et al. [J. Mod. Phys. 47 , 155 (2000)] and the other one by Chau [Quant. Inf. Comp. 11 , 721 (2011)]. Our proofs have the advantages that the necessary and sufficient conditions for equalities are apparent and that they can be readily generalized to the case of infinite-dimensional unitary operators.