Sobolev- und Sobolev-Hardy-Räume auf S1: Dualitätstheorie und Funktionalkalküle.
In this paper the analytic-spectral structure of the commutant of an invertible bilateral weighted shift operator is studied, extending known results. A class of operators is introduced, more general than the class of the rationally strictly cyclic bilateral shift [operators] which are not unicellular.
We study the relation between the sets of cyclic vectors of an unilateral bounded below weighted shift operator T and T|S where S is an invariant subspace of T. It is proved that T can not be unicellular and known results are generalized.
We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences.
We establish necessary and sufficient conditions under which each operator between Banach lattices is weakly compact and we give some consequences.