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=(T₁,...,Tₙ) 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].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-3-1,
author = {Anders Olofsson},
title = {Operator-valued n-harmonic measure in the polydisc},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {203-216},
zbl = {1071.47009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-3-1}
}
Anders Olofsson. Operator-valued n-harmonic measure in the polydisc. Studia Mathematica, Tome 162 (2004) pp. 203-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-3-1/