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Jordan operator algebras revisited
Author(s) -
Blecher David P.,
Wang Zhenhua
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800568
Subject(s) - mathematics , associative property , operator algebra , jordan algebra , algebra over a field , norm (philosophy) , hilbert space , operator (biology) , nest algebra , operator space , pure mathematics , compact operator , space (punctuation) , finite rank operator , non associative algebra , banach space , computer science , algebra representation , epistemology , philosophy , biochemistry , chemistry , programming language , repressor , gene , transcription factor , extension (predicate logic) , operating system
Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space witha 2 ∈ 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.