
It is proved that the free product state, in the reduced free product of C*-algebras, is faithful if the initial states are faithful.
GNS representation, States of selfadjoint operator algebras, free product states, Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, Mathematics - Operator Algebras, unital \(C^*\)-algebra, Functional Analysis (math.FA), Mathematics - Functional Analysis, Free probability and free operator algebras, FOS: Mathematics, free product \(C^*\)-algebra, Operator Algebras (math.OA), Analysis
GNS representation, States of selfadjoint operator algebras, free product states, Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, Mathematics - Operator Algebras, unital \(C^*\)-algebra, Functional Analysis (math.FA), Mathematics - Functional Analysis, Free probability and free operator algebras, FOS: Mathematics, free product \(C^*\)-algebra, Operator Algebras (math.OA), Analysis
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