The Noncommutative Choquet Boundary of Periodic Weighted Shifts

TL;DR

This paper investigates the noncommutative Choquet boundary and C*-envelope of operator systems generated by certain classes of operators, including periodic weighted shifts, expanding understanding of their boundary representations.

Contribution

It determines the noncommutative Choquet boundary for operator systems generated by irreducible periodic weighted unilateral shift operators, a novel result in operator theory.

Findings

Identifies the noncommutative Choquet boundary for specific operator systems.

Characterizes the C*-envelope of these systems.

Includes classes like normal, subnormal, and Toeplitz operators.

Abstract

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