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Jordan operator algebras revisited

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  • David P. Blecher
  • Zhenhua Wang

Abstract

Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space with a2∈A for all a∈A. In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative operator algebras, in particular, surprisingly much of the associative theory from several recent papers of the first author and coauthors, generalizes to Jordan operator algebras. In the present paper we complete this task, giving several results which generalize the associative case in these papers, relating to unitizations, real positivity, hereditary subalgebras, and a couple of other topics. We also solve one of the three open problems stated at the end of our earlier joint paper on Jordan operator algebras.

Suggested Citation

  • David P. Blecher & Zhenhua Wang, 2019. "Jordan operator algebras revisited," Mathematische Nachrichten, Wiley Blackwell, vol. 292(10), pages 2129-2136, October.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:10:p:2129-2136
    DOI: 10.1002/mana.201800568
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