A Characterisation for the Category of Hilbert Spaces
Year: 2025
Type: article
Abstract: The categories of real and of complex Hilbert spaces with bounded linear maps have received purely categorical characterisations by Chris Heunen and Andre Kornell. These characterisations are achieved through Solèr’s theorem, a result which shows that certain orthomodularity conditions on a Hermitian space over an involutive division ring result in a Hilbert space with the division ring being either the reals, complexes or quarternions. The characterisation by Heunen and Kornell makes use of a monoidal structure, which in turn excludes the category of quarternionic Hilbert spaces. We provide an alternative characterisation without the assumption of monoidal structure on the category. This new approach not only gives a new characterisation of the categories of real and of complex Hilbert spaces, but also the category of quaternionic Hilbert spaces.
Source: Applied Categorical Structures
Authors: Stephen Lack, Shay Tobin
Institution: Macquarie University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4408764431