Das Lomonosov-Lemma für topologische Vektorräume.
Decomposable embeddings, complete trajectories, and invariant subspaces
We produce closed nontrivial invariant subspaces for closed (possibly unbounded) linear operators, A, on a Banach space, that may be embedded between decomposable operators on spaces with weaker and stronger topologies. We show that this can be done under many conditions on orbits, including when both A and A* have nontrivial non-quasi-analytic complete trajectories, and when both A and A* generate bounded semigroups that are not stable.
Decompositions and asymptotic limit for bicontractions
The asymptotic limit of a bicontraction T (that is, a pair of commuting contractions) on a Hilbert space is used to describe a Nagy-Foiaş-Langer type decomposition of T. This decomposition is refined in the case when the asymptotic limit of T is an orthogonal projection. The case of a bicontraction T consisting of hyponormal (even quasinormal) contractions is also considered, where we have .
Definition Theory and Systems of Simultaneous Equations in the Perdual of an Operator Algebra. II.
Der spektrale Abbildungssatz für nichtanalytische Funktionalkalküle in mehreren Veränderlichen.
Derivations of Nest Algebras.
Description of invariant subspaces of Lp(μ) by multiplication operators.
Direct sums of irreducible operators
It is known that every operator on a (separable) Hilbert space is the direct integral of irreducible operators, but not every one is the direct sum of irreducible ones. We show that an operator can have either finitely or uncountably many reducing subspaces, and the former holds if and only if the operator is the direct sum of finitely many irreducible operators no two of which are unitarily equivalent. We also characterize operators T which are direct sums of irreducible operators in terms of the...
Doubly commuting submodules of the Hardy module over polydiscs
In this note we establish a vector-valued version of Beurling’s theorem (the Lax-Halmos theorem) for the polydisc. As an application of the main result, we provide necessary and sufficient conditions for the “weak” completion problem in .