QUASIANALYTIC n-TUPLES OF HILBERT SPACE OPERATORS

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, Acta Sci. Math. (Szeged) 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.