Abstract
It has been known since the pioneering work of Kadison in the early 1950s that the theory of positive maps is closely related to the Jordan algebra structure of operator algebras. In the first part of the chapter we elaborate on this structure for positive maps. One class of maps for which Jordan algebras are central, are the idempotent ones called projection maps. For those maps the image has a Jordan algebra structure, which we consider in some detail. Special emphasis will be on projections onto the Jordan algebras called spin factors, showing in particular that those projection maps have quite special properties.
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Størmer, E. (2013). Jordan Algebras and Projection Maps. In: Positive Linear Maps of Operator Algebras. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34369-8_2
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DOI: https://doi.org/10.1007/978-3-642-34369-8_2
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