Jordan operator algebras: Basic theory

Abstract

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space which are closed under the Jordan product. The discovery of the present paper is that there exists a huge and tractable theory of possibly nonselfadjoint Jordan operator algebras; they are far more similar to associative operator algebras than was suspected. We initiate the theory of such algebras.

35 pages. Corrected final version. To appear Math Nachrichten. Some of this material was described in an OTOA2016 Conference workshop lecture in ISIBANG Bangalore, December 2016. We thank the organizers of that conference for the invitation and support