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• W2052022608 abstract "We prove several characterizations of strong stability of uniformly bounded evolution families (U(t,s))t⩾s⩾0 of bounded operators on a Banach space X, i.e. we characterize the property limt→∞ ∥U(t,s)x∥=0 for all s⩾0 and all x∈X. These results are connected to the asymptotic stability of the well-posed linear nonautonomous Cauchy problemu(t)=A(t)u(t),t⩾s⩾0,u(s)=x,x∈X. In the autonomous case, i.e. when U(t,s)=T(t−s) for some C0-semigroup (T(t))t⩾0, we present, in addition, a range condition on the generator A of (T(t))t⩾0 which is sufficient for strong stability. This condition is more general than the condition in the ABLV-Theorem involving countability of the imaginary part of the spectrum of A." @default.
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• W2052022608 date "2002-08-01" @default.
• W2052022608 modified "2023-09-26" @default.
• W2052022608 title "Strong Stability of Bounded Evolution Families and Semigroups" @default.
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• W2052022608 doi "https://doi.org/10.1006/jfan.2001.3917" @default.
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