2008/10/02 by Gelu Popescu, Popescu, Gelu
Mathematics · #46L52 #47A48 #47A56 #47A60 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.0810.0451
openalex publication_date 2008/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The theory of characteristic functions for row contractions is used to determine the group Aut(B(H)n1) of all free holomorphic automorphisms of the unit ball of B(H)n. We show that the noncommutative Poisson transform commutes with the action of the automorphism group Aut(B(H)n1). This leads to a characterization of the unitarily implemented automorphisms of the Cuntz-Toeplitz algebra C^*(S1,..., Sn), which leave invariant the noncommutative disc algebra \cAn. This result provides new insight into Voiculescu's group of automorphisms of the Cuntz-Toeplitz algebra and reveals new connections with noncommutative multivariable operator theory, especially, the theory of characteristic functions for row contractions and the noncommutative Poisson transforms. We study the isometric dilations and the characteristic functions of row contractions under the action of the automorphism group Aut(B(H)n1). This enables us to obtain some results concerning the behavior of the curvature and the Euler characteristic of a row contraction under Aut(B(H)n1). We prove a maximum principle for free holomorphic functions on the noncommutative ball [B(H)n]1 and provide some extensions of the classical Schwarz lemma to our noncommutative setting.