aDepartment of Computing, Communications Technology and Mathematics, London Metropolitan University, 166-220 Holloway Road, London N7 8DB, UK;bDepartment of Mathematics, Vologda State Technical University, Vologda, Russia
Abstract:
Let be the disc algebra of all continuous complex-valued functions on the unit disc holomorphic in its interior. Functions from act on the set of all contraction operators (A1) on Hilbert spaces. It is proved that the following classes of functions from coincide: (1) the class of operator Lipschitz functions on the unit circle ; (2) the class of operator Lipschitz functions on ; and (3) the class of operator Lipschitz functions on all contraction operators. A similar result is obtained for the class of operator C2-Lipschitz functions from .