Abstract: 
\def\Ba{{\cal B}_a}\def\B{{\cal B}}
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 $$\Ba = \B
\setminus \sigma_{ap}(T).$$ 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 $\Ba = \emptyset$.

1. Université Lille 1
   UFR de Mathématiques
   UMR-CNRS 8524, Bât. M2
   F-59655 Villeneuve Cedex, France
   
2. Université Lille 1
   UFR de Mathématiques
   UMR-CNRS 8524, Bât. M2
   F-59655 Villeneuve Cedex, France
   
3. Département de Mathématiques
   et Informatique
   Faculté des Sciences de Rabat
   BP 1014 Rabat, Maroc