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linear functional; JBW-algebra; Lebesgue decomposition; normal state; trace states; state; Lebesgue decomposition of a linear functional with respect to another linear functional; support of linear functional
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.
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