Unitary asymptotes of Hilbert space operators
In this survey article we are going to present the effectiveness of the use of unitary asymptotes in the study of Hilbert space operators.
Representations with regular norm-behaviour of locally compact abelian semigroups
We prove that some regularity conditions on unbounded representations of topological abelian semigroups with countable spectral conditions induce a certain stability result extending the well-known Arendt-Batty-Lyubich-Vũ theorem.
Asymptotically cyclic quasianalytic contractions
The study of quasianalytic contractions, motivated by the hyperinvariant subspace problem, is continued. Special emphasis is put on the case when the contraction is asymptotically cyclic. New properties of the functional commutant are explored. Analytic contractions and bilateral weighted shifts are discussed as illuminating examples.
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