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Individual exponential stability for evolution families of linear and bounded operators. (English) Zbl 0990.35020
Several inequalities for the norms of a strongly continuous and exponentially bounded evolution family of bounded linear operators acting on a Banach space are obtained. These inequalities are related to a known result by R. Datko [J. Math. Anal. Appl. 32, 610-616 (1970; Zbl 0211.16802)] concerning the growth bound of a $$C_0$$-semigroup.

##### MSC:
 35B35 Stability in context of PDEs 47D06 One-parameter semigroups and linear evolution equations 35B40 Asymptotic behavior of solutions to PDEs 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory
##### Keywords:
$$C_0$$-semigroup; growth bound; spectral radius