Geodesic
Complex free spectrahedra, absolute extreme points, and dilations
Documenta mathematica, Tome 27 (2022), pp. 1275-1297.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Evert and Helton proved that real free spectrahedra are the matrix convex hulls of their absolute extreme points. However, this result does not extend to complex free spectrahedra, and we examine multiple ways in which the analogous result can fail. We also develop some local techniques to determine when matrix convex sets are not (duals of) free spectrahedra, as part of a continued study of minimal and maximal matrix convex sets and operator systems. These results apply to both the real and complex cases.
Classification : 47A20, 47A13, 46L07, 47L25
Keywords: matrix convex set, dilation, abstract operator system, matrix range 
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     author = {Passer, Benjamin},
     title = {Complex free spectrahedra, absolute extreme points, and dilations},
     journal = {Documenta mathematica},
     pages = {1275--1297},
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     volume = {27},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a34/}
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Passer, Benjamin. Complex free spectrahedra, absolute extreme points, and dilations. Documenta mathematica, Tome 27 (2022), pp. 1275-1297. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a34/