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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.

Keywords:  unitary asymptote, quasianalytic operators, commuting $n$-tuples of operators, residual sets

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