2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115350A notion of unique ergodicity relative to the fixed-point subalgebra is defined for automorphisms of unital C*-algebras. It is proved that the free shift on any reduced amalgamated free product C*-algebra is uniquely ergodic relative to its fixed-point subalgebra, as are autormorphisms of reduced group C*-algebras arising from certain automorphisms of groups. A generalization of Haagerup's inequality, yielding bounds on the norms of certain elements in reduced amalgamated free product C*-algebras, is proved.The revision (2006/08/16) includes a comment that our generalization of Haagerup's inequality can, in fact, be obtained from Ricard+Xu's results, and some other minor changesOperator Algebras46L54, 46L55text