منابع مشابه
Noncommutative Hyperbolic Geometry on the Unit Ball of B(h)
In this paper we introduce a hyperbolic (Poincaré-Bergman type) distance δ on the noncommutative open 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. It is proved that δ is invariant under the action of the free holomorphic automorphism group of [B(H)]1, i.e., δ(Ψ(X),Ψ(Y )) = δ(X, ...
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Let φ(z) = (φ1(z), · · · , φn(z)) be a holomorphic selfmap of B and ψ(z) a holomorphic function on B, where B is the unit ball of C n . Let 0 < p, s < +∞,−n− 1 < q < +∞, q+ s > −1 and α ≥ 0, this paper gives some necessary and sufficient conditions for the weighted composition operatorWψ,φ induced by φ and ψ to be bounded and compact between the space F (p, q, s) and α-Bloch space β.
متن کاملThe Dirichlet Problem on the Hyperbolic Ball
(1.2) PIH : C(Sn−1) −→ C(B) ∩ C∞(Bn), such that u = PIH f solves (1.2A) ∆Hu = 0 on B, u ∣∣ Sn−1 = f. Here, ∆H is the Laplace-Beltrami operator on B, with metric tensor (1.1). We will establish further regularity on u = PIH f when f has some further smoothness on Sn−1, and estimate du(x), in the hyperbolic metric, as x → ∂B. If n = 2, then ∆Hu = 0 if and only if ∆u = 0, where ∆ = ∂ 1 +∂ 2 2 is t...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2005
ISSN: 1370-1444
DOI: 10.36045/bbms/1110205629