Journal of Operator Theory
Volume 81, Issue 1, Winter 2019 pp. 3-20.
Quasianalytic $n$-tuples of Hilbert space operators
Authors:
Laszlo Kerchy
Author institution: Bolyai Institute, University of Szeged, Szeged, 6720, Hungary
Summary: The residual and $*$-residual parts of the unitary dilation proved to be especially useful in the study of contractions.
A more direct approach to these components, originated in B. Sz.-Nagy,
\textit{Acta Sci. Math. (Szeged)} \textbf{11}(1947),
152--157,
leads to the concept of unitary asymptote, and opens the way for generalizations to more general settings.
In this paper a systematic study of unitary asymptotes of commuting $n$-tuples of general Hilbert space operators is initiated.
Special emphasis is put on the study of the quasianalyticity property, which
constitutes homogeneous behaviour in localization, and plays a crucial role in the quest for proper hyperinvariant subspaces.
DOI: http://dx.doi.org/10.7900/jot.2017sep07.2205
Keywords: unitary asymptote, quasianalytic operators, commuting $n$-tuples of operators, residual sets
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