Exponential dichotomies and Fredholm operators
نویسندگان
چکیده
منابع مشابه
Notes on Fredholm operators
(2) If K ∈ B(X) is compact, then for all λ ∈ C \ {0}, K − λ1 is Fredholm with index zero. (3) The shift operator S± ∈ B(`p) for 1 ≤ p ≤ ∞ defined by (S±x)n = xn±1 is Fredholm with index ±1. (4) If X,Y are finite dimensional and T ∈ B(X,Y ), then by the Rank-Nullity Theorem, ind(T ) = dim(X)− dim(Y ). Lemma 3. Suppose E,F ⊆ X are closed subspaces with F finite dimensional. (1) The subspace E + F...
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Let A generate a C0–semigroup T (·) on a Banach space X such that the resolvent R(iτ, A) exists and is uniformly bounded for τ ∈ R. We show that there exists a closed, possibly unbounded projection P on X commuting with T (t). Moreover, T (t)x decays exponentially as t → ∞ for x in the range of P and T (t)x exists and decays exponentially as t→ −∞ for x in kernel of P . The domain of P depends ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1988
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1988-0958058-1