HOLOMORPHIC AUTOMORPHISMS OF NONCOMMUTATIVE POLYBALLS

作者：Popescu Gelu^*

来源：Journal of Operator Theory, 2016, 76(2): 387-448.

DOI：10.7900/jot.2015dec12.2088

• Noncommutative polyball
• automorphism
• Berezin transform
• Fock space
• creation operators
• Cuntz-Toeplitz algebra

In this paper, we study free holomorphic functions on regular polyballs B-n and provide analogues of several classical results from complex analysis such as: Abel theorem, Hadamard formula, Cauchy inequality, Schwarz lemma, and maximum principle. These results are used together with a class of noncommutative Berezin transforms to obtain a complete description of the group Aut(B-n) of all free holomorphic automorphisms of the polyball B-n. We also obtain a concrete description for the group of automorphisms of the tensor product T-n1 circle times center dot center dot center dot circle times T-nk of Cuntz-Toeplitz algebras which leave invariant the tensor product A(n1) circle times(min)center dot center dot center dot circle times(min) A(nk) of noncommutative disc algebras, which extends Voiculescu's result when k = 1.

• 出版日期2016