 If "f" attains its maximum "m"("T") on "B" at some unit vector "y", then, by the same argument used for matrices, "y" is an eigenvector of "T", with corresponding eigenvalue = .By the Banach–Alaoglu theorem and the reflexivity of "H", the closed unit ball "B" is weakly compact.Also, the compactness of "T" means (see above) that "T"