Universal Jamison spaces and Jamison sequences for C₀-semigroups

Vincent Devinck. "Universal Jamison spaces and Jamison sequences for C₀-semigroups." Studia Mathematica 214.1 (2013): 77-99. <http://eudml.org/doc/285444>.

@article{VincentDevinck2013,
abstract = {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) ∩ $ 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) ∩ $ uncountable. We also investigate the notion of Jamison sequences for C₀-semigroups and we give an arithmetic characterization of such sequences.},
author = {Vincent Devinck},
journal = {Studia Mathematica},
keywords = {partially power-bounded operators; unimodular point spectrum; Jamison sequences},
language = {eng},
number = {1},
pages = {77-99},
title = {Universal Jamison spaces and Jamison sequences for C₀-semigroups},
url = {http://eudml.org/doc/285444},
volume = {214},
year = {2013},
}

TY - JOUR
AU - Vincent Devinck
TI - Universal Jamison spaces and Jamison sequences for C₀-semigroups
JO - Studia Mathematica
PY - 2013
VL - 214
IS - 1
SP - 77
EP - 99
AB - 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) ∩ $ 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) ∩ $ uncountable. We also investigate the notion of Jamison sequences for C₀-semigroups and we give an arithmetic characterization of such sequences.
LA - eng
KW - partially power-bounded operators; unimodular point spectrum; Jamison sequences
UR - http://eudml.org/doc/285444
ER -