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• # Artykuł - szczegóły

## Studia Mathematica

2013 | 214 | 1 | 77-99

## Universal Jamison spaces and Jamison sequences for C₀-semigroups

EN

### Abstrakty

EN
An increasing sequence $(n_{k})_{k≥0}$ 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 $(n_{k})_{k≥0}$, the set $σ_{p}(T) ∩ 𝕋$ 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 $(n_{k})_{k≥0}$ which is not a Jamison sequence, there exists T ∈ ℬ(X) which is partially power-bounded with respect to $(n_{k})_{k≥0}$ and has the set $σ_{p}(T) ∩ 𝕋$ uncountable. We also investigate the notion of Jamison sequences for C₀-semigroups and we give an arithmetic characterization of such sequences.

77-99

wydano
2013

### Twórcy

autor
• Laboratoire Paul Painlevé, UMR 8524, Université des Sciences et Technologies de Lille, Cité Scientifique, 59655 Villeneuve d'Ascq Cédex, France