Constructive Gelfand duality for C*-algebras

2008/08/11 by Thierry Coquand, Dan Kučerovský, Ping Wong Ng +1 · 1 voice
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.CT #math.FA #msc:06D22 #msc:06D50 #msc:46L05

paper · pdf · doi:10.1017/s0305004109002539

published as Mathematical Proceedings of the Cambridge Philosophical society , Volume 147, Issue 02, September 2009, pp 323-337 · 6pages

arxiv published 2008/08/11 · arxiv created 2009/02/03 · openalex publication_date 2009/05/22 · arxiv updated 2010/05/26 · openalex created_date 2020/11/23 · openalex updated_date 2026/06/11

Abstract

We present a constructive proof of Gelfand duality for C*-algebras by reducing the problem to Gelfand duality for real C*-algebras.

Citations

• Completely positive linear maps on complex matrices

Discussions

• If you start with any C*-algebra, the topos T that we get from it is a Grothendieck topos (a topos of sheaves on a site), so we're good: we can do Gelfand-Naimark internal to T! 👍 However, Coquand an [bsky, 3 points, 0 comments]

Related

• Constructive Gelfand duality for non-unital commutative C*-algebras
• Computable Gelfand Duality
• Variations on a theme of Gelfand and Naimark
• C^*-algebras: The (Quantum) Path Less Traveled
• Duality for generic algebras