Bounded point evaluations for multicyclic operators

• Autorzy: M. EL Guendafi , M. Mbekhta , E. H. Zerouali
• Języki publikacji: EN

Abstrakty

EN

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 $ℬ_a = ∅$.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2005
• Tom: 67
• Numer: 1
• Strony: 199-217

Daty

wydano

2005

Twórcy

autor

M. EL Guendafi

• Université Lille 1, UFR de Mathématiques, UMR-CNRS 8524, Bât. M2, F-59655 Villeneuve Cedex, France

autor

M. Mbekhta

• Université Lille 1, UFR de Mathématiques, UMR-CNRS 8524, Bât. M2, F-59655 Villeneuve Cedex, France

autor

E. H. Zerouali

• Département de Mathématiques, et Informatique, Faculté des Sciences de Rabat, BP 1014 Rabat, Maroc

Identyfikatory

DOI

10.4064/bc67-0-16