Abstract:
In the paper, a new class of universal
$C^*$-algebras, namely, Blaschke
$C^*$-algebras, are constructed, for which the relations between generators are
defined by a family of finite Blaschke products.
Two approaches to constructing
a universal object are proposed, one of which is related to the inductive limit
of Toeplitz algebras, and the other to an isometric representation of the
uniform Blaschke algebra.
$C^*$-algebras generated by isometric representations
of a Blaschke algebra in the algebra of bounded linear operators on generalized
Hardy spaces with a probability measure and, in particular, with a Haar measure
are considered in detail.
Keywords:$C^*$-algebra, Toeplitz algebra, finite Blaschke product, inductive limit, Haar
measure.
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