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- W1514185988 abstract "Let (X, || · ||) be a Banach space. We study asymptotically bounded quasi constricted representations of an abelian semigroup ℙ in L(X), i.e. representations (Tt)t ∈ ℙ which satisfy the following conditions:i) for all x ∈ X.ii) X0 ≔ {x ∈ X : limt ∞||Ttx|| = 0} is closed and has finite codimension.We show that an asymptotically bounded representation (Tt)t ∈ ℙ is quasi constricted if and only if it has an attractor A with Hausdorff measure of noncompactness χ(A) < 1 with respect to some equivalent norm || · ||1 on X. Moreover we prove that every asymptotically weakly almost periodic quasi constricted representation (Tt)t ∈ ℙ is constricted, i.e. there exists a finite dimensional Tt)t ∈ ℙ-invariant subspace Xr such that X ≔ X0 ⊕ Xr. We apply our results to C0-semigroups." @default.
- W1514185988 created "2016-06-24" @default.
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- W1514185988 date "2002-01-01" @default.
- W1514185988 modified "2023-09-25" @default.
- W1514185988 title "Quasi Constricted Linear Representations of Abelian Semigroups on Banach Spaces" @default.
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- W1514185988 doi "https://doi.org/10.1002/1522-2616(200201)233:1<103::aid-mana103>3.0.co;2-q" @default.
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