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On Non‐Commutative Spectral Theory and Jordan Algebras
Author(s) -
Alfsen Erik M.,
Shultz Frederic W.
Publication year - 1979
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-38.3.497
Subject(s) - mathematics , algebra over a field , library science , computer science , pure mathematics
summary:In this article, a theorem is proved asserting that any linear functional defined on a JBW-algebra admits a Lebesque decomposition with respect to any normal state defined on the algebra. Then we show that the positivity (and the unicity) of this decomposition is insured for the trace states defined on the algebra. In fact, this property can be used to give a new characterization of the trace states amoungst all the normal states