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

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.