Abstract
According to a Theorem of B. Sz.-Nagy and C. Foiaş, every strongly continuous semigroup of contraction operators on a Hilbert space, can be decomposed into a completely non unitary part and a unitary part. In this note we wish to show that by appropriately perturbing its generator, a contraction semigroup can be reduced to a completely non unitary one. In control theory, such a perturbation is related to the so called state feedback, and the reduction presented here has application in the problem of stabilizing linear control systems on a Hilbert space. This will be briefly discussed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
