Abstract
Inspired by a well-known characterization of the index of an inclusion of II factors due to Pimsner and Popa, we define an index-type invariant for inclusions of operator systems. We compute examples of this invariant, show that it is multiplicative under minimal tensor products, and explain how it generalizes the quantum Lovász theta invariant for a matricial system defined by Duan, Severini, and Winter.
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