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 (https://doi.org/10.4204/EPTCS.266.13)
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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.
ORCID iDs
Dunne, Kevin ORCID: https://orcid.org/0000-0003-1148-5202;-
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Item type: Article ID code: 64969 Dates: DateEvent27 February 2018Published29 May 2017AcceptedSubjects: 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: 02 Oct 2024 00:31 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/64969