Hyperbolic Geometry on the Unit Ball of B(h) and Dilation Theory
نویسنده
چکیده
In this paper we continue our investigation concerning the hyperbolic geometry on the noncommutative ball [B(H)]−1 := n (X1, . . . ,Xn) ∈ B(H) n : ‖X1X ∗ 1 + · · ·+XnX ∗ n‖ 1/2 ≤ 1 o , where B(H) is the algebra of all bounded linear operators on a Hilbert space H, and its implications to noncommutative function theory. The central object is an intertwining operator LB,A of the minimal isometric dilations of A,B ∈ [B(H)]−1 , which establishes a strong connection between noncommutative hyperbolic geometry on [B(H)]−1 and multivariable dilation theory. The goal of this paper is to study the operator LB,A and its connections to the hyperbolic metric δ on the Harnack parts ∆ of [B(H) ]−1 . In particular, we show that δ(A,B) = lnmax n
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