Bounded point evaluations for multicyclic operators
Volume 67 / 2005
Banach Center Publications 67 (2005), 199-217
MSC: Primary 47B; Secondary 47A.
DOI: 10.4064/bc67-0-16
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 ($\beta$), then $${\cal B}_a = {\cal B} \setminus \sigma_{ap}(T).$$ 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 ${\cal B}_a = \emptyset$.
