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Stability of one parameter Co-semigroups on hereditarily indecomposable Banach spaces

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Abstract (2. Language): 
The main result is the following stability theorem: Let T — (T{t))t>o be a bounded Co-semigroup on a hereditarily indecompdsable Banach space X, with the infinitesimal generator A and domain D(A), if we denote by A* the adjoint of A and by ap(A") the point spectrum of A*, then T is strongly stable (which means lim ||T(i)a:|| = 0, Va; € X), if t —> oo and only if av(A*) D iTEL — 0
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