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 ![]() | Item type: | Article |
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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: | 21 Jan 2021 10:20 |
Related URLs: | |
URI: | https://strathprints.strath.ac.uk/id/eprint/64969 |
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