Bounded point evaluations for multicyclic operators

M. EL Guendafi, M. Mbekhta, and E. H. Zerouali. "Bounded point evaluations for multicyclic operators." Banach Center Publications 67.1 (2005): 199-217. <http://eudml.org/doc/282351>.

@article{M2005,
abstract = {Let T be a multicyclic operator defined on some Banach space. Bounded point evaluations and analytic bounded point evaluations for T are defined to generalize the cyclic case. We extend some known results on cyclic operators to the more general setting of multicyclic operators on Banach spaces. In particular we show that if T satisfies Bishop’s property (β), then $ℬ_a = ℬ ∖ σ_\{ap\}(T)$. We introduce the concept of analytic structures and we link it to different spectral quantities. We apply this concept to retrieve in an easy way a theorem of D. Herrero and L. Rodman: the set of cyclic n-tuples for a multicyclic operator T is dense if and only if $ℬ_a = ∅$.},
author = {M. EL Guendafi, M. Mbekhta, E. H. Zerouali},
journal = {Banach Center Publications},
keywords = {multicyclic operator; analytic structure; point evaluation; singular spectrum; Bishop’s property },
language = {eng},
number = {1},
pages = {199-217},
title = {Bounded point evaluations for multicyclic operators},
url = {http://eudml.org/doc/282351},
volume = {67},
year = {2005},
}

TY - JOUR
AU - M. EL Guendafi
AU - M. Mbekhta
AU - E. H. Zerouali
TI - Bounded point evaluations for multicyclic operators
JO - Banach Center Publications
PY - 2005
VL - 67
IS - 1
SP - 199
EP - 217
AB - Let T be a multicyclic operator defined on some Banach space. Bounded point evaluations and analytic bounded point evaluations for T are defined to generalize the cyclic case. We extend some known results on cyclic operators to the more general setting of multicyclic operators on Banach spaces. In particular we show that if T satisfies Bishop’s property (β), then $ℬ_a = ℬ ∖ σ_{ap}(T)$. We introduce the concept of analytic structures and we link it to different spectral quantities. We apply this concept to retrieve in an easy way a theorem of D. Herrero and L. Rodman: the set of cyclic n-tuples for a multicyclic operator T is dense if and only if $ℬ_a = ∅$.
LA - eng
KW - multicyclic operator; analytic structure; point evaluation; singular spectrum; Bishop’s property 
UR - http://eudml.org/doc/282351
ER -