A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum

Batty, Charles; Brzeźniak, Zdzisław; Greenfield, David

Batty, Charles ; Brzeźniak, Zdzisław ; Greenfield, David

Studia Mathematica, Tome 119 (1996), p. 167-183 / Harvested from The Polish Digital Mathematics Library

Résumé

Let T be a semigroup of linear contractions on a Banach space X, and let $X_{s} (T) = x \in X : l i m_{s \to \infty} ∥ T (s) x ∥ = 0$ . 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 $l i m_{s} ∥ T (s) x ∥ = i n f ∥ x - y ∥ : y \in X_{s} (T)$ for each x in X.

Publié le : 1996-01-01

Zbl 0862.47020

EUDML-ID : urn:eudml:doc:216349

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     author = {Charles Batty and Zdzis\l aw Brze\'zniak and David Greenfield},
     title = {A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {167-183},
     zbl = {0862.47020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv121i2p167bwm}
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Batty, Charles; Brzeźniak, Zdzisław; Greenfield, David. A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum. Studia Mathematica, Tome 119 (1996) pp. 167-183. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv121i2p167bwm/

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