a EDF R&D, Départment OSIRIS, 1 avenue du général de Gaulle, 92140 Clamart, France b Delft Institute of Applied Mathematics, Delft University of Technology, Fac.EEMCS, Mekelweg 4, 2628CD Delft, The Netherlands c School of Informatics and Engineering, The Flinders University of South Australia, Bedford Park, 5042 SA, Australia
Abstract:
We present a systematic characterization of the domain of a generator of a one parameter group on certain C∗-subalgebras of via finite-dimensional estimates. Our approach yields an example of a densely defined closed symmetric derivation on a C∗-subalgebras of whose domain is not closed with respect to the C1-functional calculus. This completes and complements the earlier example of McIntosh (J. Funct. Anal. 30 (1977) 264). Our methods are partly based on the theory of adjoint C0-semigroups.
via finite-dimensional estimates. Our approach yields an example of a densely defined closed symmetric derivation on a C∗-subalgebras of 
whose domain is not closed with respect to the C1-functional calculus. This completes and complements the earlier example of McIntosh (J. Funct. Anal. 30 (1977) 264). Our methods are partly based on the theory of adjoint C0-semigroups.