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This expository article gives a survey of matrix convex sets, a natural generalization of convex sets to the noncommutative (dimension-free) setting, with a focus on their extreme points. Mirroring the classical setting, extreme points play an import
Externí odkaz:
http://arxiv.org/abs/2405.07924
We study the local-triviality dimensions of actions on $C^*$-algebras, which are invariants developed for noncommutative Borsuk-Ulam theory. While finiteness of the local-triviality dimensions is known to guarantee freeness of an action, we show that
Externí odkaz:
http://arxiv.org/abs/2403.06767
Autor:
Maierhofer, Dominik, van Karsbergen, Vincent, Potrč Obrecht, Tajda, Ruschi Mendes Saade, Marcella, Gingrich, Simone, Streicher, Wolfgang, Erb, Karl-Heinz, Passer, Alexander
Publikováno v:
In Sustainable Production and Consumption November 2024 51:612-627
Autor:
Alaux, Nicolas, Marton, Christopher, Steinmann, Jacob, Maierhofer, Dominik, Mastrucci, Alessio, Petrou, Danai, Potrč Obrecht, Tajda, Ramon, Delphine, Le Den, Xavier, Allacker, Karen, Passer, Alexander, Röck, Martin
Publikováno v:
In Journal of Environmental Management November 2024 370
Autor:
Passer, Benjamin
Publikováno v:
Doc. Math. 27 (2022), 1275-1297
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.
Externí odkaz:
http://arxiv.org/abs/2108.09185
Publikováno v:
In Journal of Cleaner Production 25 June 2024 459
Autor:
Toll, Brandon J., Yolcu, Yagiz U., Passer, Joel Z., Yew, Andrew Y., Magge, Subu N., Ghogawala, Zoher, Whitmore, Robert G.
Publikováno v:
In World Neurosurgery June 2024 186:e391-e397
Autor:
Davidson, Kenneth R., Passer, Benjamin
Publikováno v:
Int. Math. Res. Not. IMRN 7 (2022), 5037-5070
We use Arveson's notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets which admit minimal presentations. A fully compressed separable operator system necessarily generates the C*-env
Externí odkaz:
http://arxiv.org/abs/2005.11582
Akademický článek
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Autor:
Passer, Benjamin, Paulsen, Vern I.
Publikováno v:
J. Operator Theory 85:2 (2021), 547-568
For finite-dimensional operator systems $\mathcal{S}_{\mathsf T}$, ${\mathsf T} \in B({\mathcal H})^d$, we show that the local lifting property and $1$-exactness of $\mathcal{S}_{\mathsf T}$ may be characterized by measurements of the disparity betwe
Externí odkaz:
http://arxiv.org/abs/1912.06279