Geodesic
Operator-valued $n$-harmonic measure in the polydisc
Anders Olofsson1
1 Falugatan 22 1tr SE-113 32 Stockholm, Sweden
Studia Mathematica, Tome 163 (2004) no. 3, pp. 203-216

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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].
DOI : 10.4064/sm163-3-1
Keywords: operator valued multi variable poisson type integral studied section nbsp obtain equivalent condition existence so called regular unitary dilation n tuple dots commuting contractions development section nbsp contains proof classical dilation result brehmer nbsp nagy halperin section nbsp turn boundary behavior operator valued poisson integral results obtained section improve earlier result proved curto h vasilescu nbsp

Anders Olofsson 1

1 Falugatan 22 1tr SE-113 32 Stockholm, Sweden 
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Anders Olofsson. Operator-valued $n$-harmonic measure
 in the polydisc. Studia Mathematica, Tome 163 (2004) no. 3, pp. 203-216. doi: 10.4064/sm163-3-1

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