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

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    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.

    Creators(s): Dunne, Kevin ORCID logoORCID: https://orcid.org/0000-0003-1148-5202;
    Item type:Article
    ID code:64969
    Keywords:generalised topos approach, quantum theory, dagger-kernel approach, h*-algebras, Electronic computers. Computer science, Computer Science(all)
    Subjects:Science > Mathematics > Electronic computers. Computer science
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:01 Aug 2018 14:38
    Last modified:07 Sep 2020 04:10
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/64969
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