-Derivations of Operator Algebras and an Application

Let be a bijective bounded linear operator on a Banach algebra A: In this talk, we closely examine the concept of -one parameter groups of bounded linear operators as a generalization of one parameter groups and analyze their basic properties. We also, describe a -C -dynamical system as a uniformly continuous -one parameter group of -linear automorphisms on a C -algebra and associate with each so-called -C -dynamical system a - derivation, named as its in nitesimal generator. Finally, as an application, we characterize each -C -dynamical system on the concrete C -algebra A := B(H); where H is a Hilbert space.