Abstract

In the paper we introduce the notion of the Blaschke \(C^{*}\)-algebra and we consider the isometric representations of uniform Blaschke algebra. We extend the Coburn’s Theorem for a family of non-unitary isometries connected by a family of finite Blaschke products. We show that the Blaschke \(C^{*}\)-algebra is isomorphic to the inductive limit of Toeplitz algebras, as well as the (non commutative) \(C^{*}\)-algebra generated by a unital isometric representation of the uniform Blaschke algebra by multiplications in the respective Hardy space.

中文翻译：

---

Blaschke $$ \ boldsymbol {C} ^ {\ boldsymbol {*}} $$-代数

摘要

在本文中，我们介绍了Blaschke \（C ^ {*} \）-代数的概念，并考虑了均匀Blaschke代数的等距表示。我们将Coburn定理扩展为通过有限的Blaschke乘积族连接的非-一性等距族。我们证明Blaschke \（C ^ {*} \）-代数同等同于Toeplitz代数的归纳极限，以及由等轴测图生成的（非可交换）\（C ^ {*} \）-代数相应的Hardy空间中的乘法表示均匀Blaschke代数。