Ergodic Properties for Regular A-Contractions

The current article pleads for the possibility to obtain an orthogonal decomposition of a Hilbert space which is induced by a regular A-contraction defined in [9, 10], A being a positive operator on . The decomposition generalizes the well-known decomposition related to a contraction T of , which gives the ergodic character of T. This decomposition is being used to prove certain versions for regular A-contractions of the mean ergodic theorem, as well as a version of Patil’s theorem from [8]. Also, we characterize the solutions of corresponding functional equations in the range of A^1/2, by analogy with the result of Lin-Sine in [7].