Abstract characterizations of compact matrix convex sets and base norm spaces (classical and nc) are developed, yielding new dual characterizations of operator systems.
Real Non-Commutative Convexity I
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abstract
We initiate the theory of real noncommutative (nc) convex sets, the real case of the recent and profound complex theory developed by Davidson and Kennedy. The present paper focuses on the real case of the topics from the first several sections of their Memoir. Later results will be discussed in future papers. We develop here some of the infrastructure of real nc convexity, giving many foundational structural results for real operator systems and their associated nc convex sets, and elucidate how the complexification interacts with the basic convexity theory constructions. Several new features appear in the real case, including the novel notion of the complexification of a nc convex set.
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math.OA 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Compact convex sets and bases--classical and noncommutative
Abstract characterizations of compact matrix convex sets and base norm spaces (classical and nc) are developed, yielding new dual characterizations of operator systems.