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The noncommutative Choquet boundary and the C*-envelope of operator systemsof the form Span{1,T,T*}, where T is a Hilbert space operator with normal-likefeatures, are studied. Such operators include normal operators, k-normaloperators, subnormal operators, and Toeplitz operators. Our main result is thedetermination of the noncommutative Choquet boundary for an operator systemgenerated by an irreducible periodic weighted unilateral shift operator.

The Noncommutative Choquet Boundary of Periodic Weighted Shifts