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Completeness of Gelfand-Neumark-Segal inner product space on Jordan algebras

In: Mathematica Slovaca, vol. 66, no. 2
Jan Hamhalter - Ekaterina Turilova

Details:

Year, pages: 2016, 459 - 468
Keywords:
GNS representation, Jordan Banach algebras, completeness, pure states
About article:
The paper deals with inner product spaces generated by states on Jordan algebras. We show an interplay between completeness of the Gelfand-Neumark-Segal representation space, geometric properties of states on Jordan algebras, structure of irreducible Jordan representations, and properties of normal states on second duals of Jordan algebras. We prove that if the GNS representation space is complete, then given state must be a convex combination of pure states. On the other hand, we analyze structure of inner product spaces arising from states on spin factors and Type $In$, $n≥ 4$, factors, showing their completeness as a consequence.
How to cite:
ISO 690:
Hamhalter, J., Turilova, E. 2016. Completeness of Gelfand-Neumark-Segal inner product space on Jordan algebras. In Mathematica Slovaca, vol. 66, no.2, pp. 459-468. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0150

APA:
Hamhalter, J., Turilova, E. (2016). Completeness of Gelfand-Neumark-Segal inner product space on Jordan algebras. Mathematica Slovaca, 66(2), 459-468. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0150
About edition:
Published: 1. 4. 2016