Faithfulness of free product states
Kenneth J. Dykema
TL;DR
This paper proves that in the reduced free product of C*-algebras, the free product state remains faithful if the original states are faithful, ensuring the preservation of faithfulness under free product operations.
Contribution
It establishes the faithfulness of free product states in the reduced free product of C*-algebras when initial states are faithful, a result previously unconfirmed.
Findings
Free product state is faithful if initial states are faithful.
Faithfulness is preserved under reduced free product construction.
Provides theoretical foundation for analyzing free product states.
Abstract
It is proved that the free product state, in the reduced free product of C*-algebras, is faithful if the initial states are faithful.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Algebra and Logic · Advanced Topics in Algebra