Two-Parameter σ-C∗-Dynamical Systems and Application

Let A be a C∗-algebra and σ be a bounded linear ∗- endomorphism on A. Introducing the notions of ∗-σ-derivations and two-parameter σ-C∗-dynamical sytems, we correspond to each so-called two-parameter σ-C∗-dynamical system a pair of σ-derivations, named as its infinitesimal generator. Using the computation formula for σ- derivations, we deal with the converse under mild conditions. Finally, as an application, we characterize each so-called two parameter σ-C∗- dynamical system on the concrete C∗-algebra A := B(H)×B(H), where H is a Hilbert space and σ is the linear ∗-endomorphism σ(S, T ) = (0, T ).