Faithfulness of free products refers to a property of free products of von Neumann algebras where the resulting algebra retains the property of faithfully representing states from the individual algebras. This means that if a state is faithful in one of the contributing algebras, it remains faithful in the free product, ensuring that the structure and properties of the original algebras are preserved in a meaningful way. This concept is essential when considering how free products combine algebras while maintaining their integrity and relationships with their respective states.
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