DYNAMICAL SYSTEMS ON HILBERT MODULES OVER LOCALLY C*-ALGEBRAS

Let A be a locally C*-algebra and S(A) be the family of continuous C*-seminorms and let epsilon be a Hilbert A-module. We prove that every dynamical system of unitary operators on epsilon defines a dynamical system of automorphisms on the compact operators on epsilon and show that under certain conditions, the converse is true. We define a generalized derivation on epsilon and prove that if epsilon is a full Hilbert A-module and delta : epsilon -> epsilon is a bounded generalized derivation, then delta(p) : epsilon(p) -> epsilon(p) is a generalized derivation on the Hilbert module epsilon(p) over the C*-algebra A(p) for each p is an element of S(A).