On the structure of abstract h*-algebras

Dunne, Kevin (2018) On the structure of abstract h*-algebras. Electronic Proceedings in Theoretical Computer Science, EPTCS, 266. pp. 197-208. ISSN 2075-2180

[thumbnail of Dunne-EPTCS-2017-On-the-structure-of-abstract-h-algebras]
Preview
 Text (Dunne-EPTCS-2017-On-the-structure-of-abstract-h-algebras)
Dunne_EPTCS_2017_On_the_structure_of_abstract_h_algebras.pdf
Final Published Version
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo
Download (167kB)| Preview

    Abstract

    Previously we have shown that the topos approach to quantum theory of Doering and Isham can be generalised to a class of categories typically studied within the monoidal approach to quantum theory of Abramsky and Coecke. In the monoidal approach to quantum theory H*-algebras provide an axiomatisation of states and observables. Here we show that H*-algebras naturally correspond with the notions of states and observables in the generalised topos approach to quantum theory. We then combine these results with the dagger-kernel approach to quantumlogic of Heunen and Jacobs, which we use to prove a structure theorem for H*-algebras. This structure theorem is a generalisation of the structure theorem of Ambrose for H*-algebras the category of Hilbert spaces.

    ORCID iDs

    Dunne, Kevin ORCID logoORCID: https://orcid.org/0000-0003-1148-5202;
    CORE (COnnecting REpositories)