Abstract
We investigate for a bounded semigroup of linear operators S on a Banach space E and a vector x∈E, when relative compactness of S(I−T)x for every T∈S implies relative compactness of the orbit Sx. In particular, we derive characterizations of separable Banach spaces not containing c0 and of reflexivity of Banach spaces with a Schauder basis in terms of such compactness results.
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