Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)

Orthogonality spaces allowing gradual transitions

Authors
Thomas Vetterlein
Corresponding Author
Thomas Vetterlein
Available Online August 2019.
DOI
https://doi.org/10.2991/eusflat-19.2019.29How to use a DOI?
Keywords
Orthogonality space Real Hilbert space Foundations of quantum mechanics
Abstract
We consider orthogonality spaces subjected to the condition that gradual transitions between any two elements are possible. More precisely, given elements e and f, we require a homomorphism from the unit circle to the automorphism group to exist such that one of these automorphisms maps e to f, and any of these automorphisms leaves the elements orthogonal to e and f fixed. A natural example is the collection of one-dimensional subspaces of a real Hilbert space, endowed with the usual orthogonality relation. We show that the general case is closely related to this example.
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Proceedings
11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)
Part of series
Atlantis Studies in Uncertainty Modelling
Publication Date
August 2019
ISBN
978-94-6252-770-6
ISSN
2589-6644
DOI
https://doi.org/10.2991/eusflat-19.2019.29How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Thomas Vetterlein
PY  - 2019/08
DA  - 2019/08
TI  - Orthogonality spaces allowing gradual transitions
BT  - 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)
PB  - Atlantis Press
SP  - 192
EP  - 197
SN  - 2589-6644
UR  - https://doi.org/10.2991/eusflat-19.2019.29
DO  - https://doi.org/10.2991/eusflat-19.2019.29
ID  - Vetterlein2019/08
ER  -