PIRSA:14040140

Categories of Convex Sets and C*-Algebras

Furber, R. (2014). Categories of Convex Sets and C*-Algebras. Perimeter Institute. https://pirsa.org/14040140

Furber, Robert. Categories of Convex Sets and C*-Algebras. Perimeter Institute, Apr. 15, 2014, https://pirsa.org/14040140 

          @misc{ pirsa_PIRSA:14040140,
            doi = {10.48660/14040140},
            url = {https://pirsa.org/14040140},
            author = {Furber, Robert},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Categories of Convex Sets and C*-Algebras},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {apr},
            note = {PIRSA:14040140 see, \url{https://pirsa.org}}
          }

Robert Furber Radboud Universiteit Nijmegen

DOI 10.48660/14040140
Collection
Talk Type Scientific Series
Subject

Abstract

The start of the talk will be an outline how the ordinary notions of quantum theory translate into the category of C*-algebras, where there are several possible choices of morphisms. The second half will relate this to a category of convex sets used as state spaces. Alfsen and Shultz have characterized the convex sets arising from state spaces C*-algebras and this result can be applied to get a categorical equivalence between C*-algebras and state spaces of C*-algebras which is a generalization of the equivalence between the Schroedinger and Heisenberg pictures.