A decomposition theorem for generators of strongly continuous groups on Hilbert spaces

摘要

For the generator A of a strongly continuous group on a Hilbert space, we modify Liapunov's method of changing the scalar product to obtain a decomposition A = B + C with B skew-adjoint and C bounded and selfadjoint (with respect to the new scalar product). This yields a new proof of the fact that A has bounded H-infinity-calculi on vertical strips. Furthermore we show that, with respect to the new scalar product, A(2) can be obtained by a closed sectorial form in the sense of Kato.