THE BISHOP–PHELPS–BOLLOBÁS PROPERTY FOR HERMITIAN FORMS ON HILBERT SPACES

In this paper, we prove that the Bishop–Phelps–Bollobás Theorem holds for hermitian forms on a complex Hilbert space and for symmetric bilinear forms on a real or complex Hilbert space. The Bishop–Phelps–Bollobás Theorem for operators in the Schatten–von Neumann classes is also obtained.