A Class of Contractions in Hilbert Space and Applications
We characterize the bounded linear operators T in Hilbert space which satisfy T = βI + (1-β)S where β ∈ (0,1) and S is a contraction. The characterizations include a quadratic form inequality, and a domination condition of the discrete semigroup by the continuous semigroup . Moreover, we give a stronger quadratic form inequality which ensures that . The results apply to large classes of Markov operators on countable spaces or on locally compact groups.