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

作者：Haase M^*

来源：Journal of Operator Theory, 2004, 52(1): 21-37.

• co-group
• Liapunov's direct method
• H-infinity-calculus
• cosine function
• square root problem

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.

• 出版日期2004