11 papers
Compact convex sets and bases--classical and noncommutative
David P. Blecher, Christiaan H. Pretorius
Matrix and noncommutative convexity constitute an important area of modern noncommutative analysis and have found significant applications in mathematical physics. In the first par…
Real decomposable maps on operator systems
David P. Blecher, Christiaan H. Pretorius
We initiate and study the theory of ``real decomposable maps" between real operator systems. Formally, this is new even in the complex case, which hitherto has restricted itself to…
Real Non-Commutative Convexity I
David P. Blecher, Caleb McClure
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…
Real Noncommutative Convexity II: Extremality and nc convex functions
David P. Blecher, Caleb Becker McClure
We continue the development of real noncommutative (nc) convexity, building on the recent and profound complex theory of Davidson and Kennedy. The present paper focuses on the theo…
Base norm spaces--classical, complex, and noncommutative
David P. Blecher, Damon M. Hay
We generalize the theory of base norm spaces to the complex case, and further to the noncommutative setting relevant to `quantum convexity'. In particular, we establish the duality…
Regularity of compact convex sets--classical and noncommutative
David P. Blecher
The classical theory of regularity of embeddings of compact convex sets was developed in the 1970s, exclusively in the real case, and even there it does not appear to have been sta…