some image logo

HOME

SEARCH

CURRENT ISSUE

REGULAR ISSUES

   Volume 1 (2005)

   Volume 2 (2006)

   Volume 3 (2007)

   Volume 4 (2008)

   Volume 5 (2009)

   Volume 6 (2010)

   Volume 7 (2011)

   Volume 8 (2012)

   Volume 9 (2013)

   Volume 10 (2014)

   Volume 11 (2015)

      Issue 1

      Issue 2

      Issue 3

      Issue 4

   Volume 12 (2016)

   Volume 13 (2017)

SPECIAL ISSUES

SURVEY ARTICLES

AUTHORS

ABOUT

SERVICE

LOGIN

FAQ

SUPPORT

CONTACT

VOLUME 11, ISSUE 2, PAPER 5


From Kleisli Categories to Commutative C*-algebras: Probabilistic Gelfand Duality

©Robert W. J. Furber, Radboud University Nijmegen
©Bart P. F. Jacobs, Radboud University Nijmegen

Abstract
C*-algebras form rather general and rich mathematical structures that can be studied with different morphisms (preserving multiplication, or not), and with different properties (commutative, or not). These various options can be used to incorporate various styles of computation (set-theoretic, probabilistic, quantum) inside categories of C*-algebras. At first, this paper concentrates on the commutative case and shows that there are functors from several Kleisli categories, of monads that are relevant to model probabilistic computations, to categories of C*-algebras. This yields a new probabilistic version of Gelfand duality, involving the "Radon" monad on the category of compact Hausdorff spaces. We then show that the state space functor from C*-algebras to Eilenberg-Moore algebras of the Radon monad is full and faithful. This allows us to obtain an appropriately commuting state-and-effect triangle for C*-algebras.

Publication date: June 10, 2015

Full Text: PDF | PostScript
DOI: 10.2168/LMCS-11(2:5)2015

Hit Counts: 4265

Creative Commons