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A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum

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J. K. Batty C., Brzeźniak Z., Greenfield D. A.

Studia Mathematica

1996

tom 121

nr 2

167-183

Let T be a semigroup of linear contractions on a Banach space X, and let $X_{s}(T) = {x ∈ X : lim_{s→∞} ∥T(s)x∥ = 0}$. Then $X_{s}(T)$ is the annihilator of the bounded trajectories of T*. If the unitary spectrum of T is countable, then $X_{s}(T)$ is the annihilator of the unitary eigenvectors of T*, and $lim_{s} ∥T(s)x∥ = inf{∥x-y∥ : y ∈ X_{s}(T)}$ for each x in X.

Ograniczanie wyników

1 Studia Mathematica

1 Brzeźniak Z.

1 Greenfield D. A.

1 J. K. Batty C.

1 1996

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A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum