Universal Jamison spaces and Jamison sequences for C₀-semigroups

Vincent Devinck

Vincent Devinck

Studia Mathematica, Tome 215 (2013), p. 77-99 / Harvested from The Polish Digital Mathematics Library

Résumé

An increasing sequence ${(n_{k})}_{k \geq 0}$ of positive integers is said to be a Jamison sequence if for every separable complex Banach space X and every T ∈ ℬ(X) which is partially power-bounded with respect to ${(n_{k})}_{k \geq 0}$ , the set $σ_{p} (T) \cap$ is at most countable. We prove that for every separable infinite-dimensional complex Banach space X which admits an unconditional Schauder decomposition, and for any sequence ${(n_{k})}_{k \geq 0}$ which is not a Jamison sequence, there exists T ∈ ℬ(X) which is partially power-bounded with respect to ${(n_{k})}_{k \geq 0}$ and has the set $σ_{p} (T) \cap$ uncountable. We also investigate the notion of Jamison sequences for C₀-semigroups and we give an arithmetic characterization of such sequences.

Publié le : 2013-01-01

Zbl 06150599

EUDML-ID : urn:eudml:doc:285444

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     author = {Vincent Devinck},
     title = {Universal Jamison spaces and Jamison sequences for C0-semigroups},
     journal = {Studia Mathematica},
     volume = {215},
     year = {2013},
     pages = {77-99},
     zbl = {06150599},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-1-5}
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Vincent Devinck. Universal Jamison spaces and Jamison sequences for C₀-semigroups. Studia Mathematica, Tome 215 (2013) pp. 77-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-1-5/