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Jordan operator algebras: basic theory
Author(s) -
Blecher David P.,
Wang Zhenhua
Publication year - 2018
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.201700178
Subject(s) - mathematics , jordan algebra , nest algebra , operator algebra , associative property , von neumann's theorem , algebra over a field , compact operator , operator space , hilbert space , operator (biology) , quasinormal operator , finite rank operator , norm (philosophy) , compact operator on hilbert space , pure mathematics , reflexive operator algebra , operator norm , operator theory , multiplication operator , non associative algebra , banach space , algebra representation , computer science , repressor , law , chemistry , biochemistry , political science , transcription factor , programming language , extension (predicate logic) , gene
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.