Defines real decomposable maps on real operator systems, uncovers a new term in their decomposition that forms a novel class of maps, and verifies real analogs of known results on weak expectation property and injectivity.
Noncommutative Cho quet theory
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Initiates theory of real nc convex sets with foundational structural results for real operator systems and introduces complexification of nc convex sets.
A general lifting framework called the royal road theorem shows that automatic analyticity, monotonicity, and convexity results in multiple noncommuting variables follow from the one-variable case, with applications to noncommutative Löwner and Kraus theorems over operator systems.
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The royal road to automatic noncommutative real analyticity, monotonicity, and convexity
A general lifting framework called the royal road theorem shows that automatic analyticity, monotonicity, and convexity results in multiple noncommuting variables follow from the one-variable case, with applications to noncommutative Löwner and Kraus theorems over operator systems.