Orthogonality spaces allowing gradual transitions

DOI

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.

Copyright

© 2019, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Thomas Vetterlein
PY  - 2019/08
DA  - 2019/08
TI  - Orthogonality spaces allowing gradual transitions
BT  - Proceedings of the 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  - 10.2991/eusflat-19.2019.29
ID  - Vetterlein2019/08
ER  -