Blaschke C* -algebras

Abstract

© 2020, PleiadesT Publishing,T Ltd. 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.