Operator-valued $n$-harmonic measure in the polydisc
Volume 163 / 2004
Studia Mathematica 163 (2004), 203-216
MSC: Primary 47A25; Secondary 31C99.
DOI: 10.4064/sm163-3-1
Abstract
An operator-valued multi-variable Poisson type integral is studied. In Section 2 we obtain a new equivalent condition for the existence of a so-called regular unitary dilation of an $n$-tuple $T=(T_1,\dots,T_n)$ of commuting contractions. Our development in Section 2 also contains a new proof of the classical dilation result of S. Brehmer, B. Sz.-Nagy and I. Halperin. In Section 3 we turn to the boundary behavior of this operator-valued Poisson integral. The results obtained in this section improve upon an earlier result proved by R. E. Curto and F.-H. Vasilescu in [3].
