科研之友
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摘要
We examine the completely isometric automorphisms of a free product of noncommutative disc algebras. It will be established that such an automorphism is given simply by a completely isometric automorphism of each component of the free product and a permutation of the components. This mirrors a similar fact in topology concerning biholomorphic automorphisms of product spaces with nice boundaries due to Rudin, Ligocka, and Tsyganov. This paper is also a study of multivariable dynamical systems by their semicrossed product algebras. A new form of dynamical system conjugacy is introduced, and is shown to completely characterize the semicrossed-product algebra. This is proven by using the rigidity of free-product automorphisms established in the first part of the paper. Last, a representation theory is developed to determine when the semicrossed-product algebra and the tensor algebra of a dynamical system are completely isometrically isomorphic.
- 出版日期2016
