Three characterisations of the sequential product
Abstract
It has already been established that the properties required of an abstract sequential product as introduced by Gudder and Greechie are not enough to characterise the standard sequential product a ◦b =√{a }b √{a } on an operator algebra. We give three additional properties, each of which characterises the standard sequential product on either a von Neumann algebra or a Euclidean Jordan algebra. These properties are (1) invariance under the application of unital order isomorphisms, (2) symmetry of the sequential product with respect to a certain inner product, and (3) preservation of invertibility of the effects. To give these characterisations, we first have to study convex σsequential effect algebras. We show that these objects correspond to unit intervals of spectral order unit spaces with a homogeneous positive cone.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 August 2018
 DOI:
 10.1063/1.5031089
 arXiv:
 arXiv:1803.08453
 Bibcode:
 2018JMP....59h2202V
 Keywords:

 Mathematics  Operator Algebras;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 18 pages + 2 page appendix