Stability Conditions for Perturbed Semigroups on a Hilbert Space via Commutators

Authors : Michael GİL`

Pages : 129-134

Doi:10.33434/cams.508305

View : 46 | Download : 10

Publication Date : 2019-06-27

Article Type : Research Paper

Abstract :Let $A$ and $B$ be linear operators on a Hilbert space. Let $A$ and $A+B$ generate $C_0$-semigroups $e^{tA}$ and $e^{tinsert ignore into journalissuearticles values(A+B);}$, respectively, and $e^{tA}$ be exponentially stable. We establish exponential stability conditions for $e^{tinsert ignore into journalissuearticles values(A+B);}$ in terms of the commutator $AB-BA$, assuming that it has a bounded extension. Besides, $B$ can be unbounded.
Keywords : Hilbert space, Commutator, Semigroups, Stability

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