Universal Jamison spaces and Jamison sequences for C₀-semigroups

• Autorzy: Vincent Devinck
• Języki publikacji: 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.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 214
• Numer: 1
• Strony: 77-99

Daty

wydano

2013

Twórcy

autor

Vincent Devinck

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

Identyfikatory

DOI

10.4064/sm214-1-5