Let us recall some terminology concerning mappings between Hilbert spaces.
Definition 4.1.1 Let H, H′ be Hilbert spaces.
|(i)||f : H → H′ is bounded if it maps bounded sets into bounded sets.|
|(ii)||f : H → H′ is positive homogeneous of degree α > 0 if
Taking u = 0 and s = 0 gives f (0) = 0. When α = 1 we will simply say that f is positive homogeneous.
|(iii)||f : H → H is monotone if
|(iv)||f ∈ C(H, H) is a potential operator if there is a F ∈ C1(H, ℝ), called a potential for f , such that