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We show that the involution θ(a ⊗ b) = a * ⊗ b * on the Haagerup tensor product A ⊗ H B of C * -algebras A and B is an isometry if and only if A and B are commutative. The involutive Banach algebra A ⊗ H A arising from the involution a ⊗ b → b * ⊗ a * is also studied.doi:10.1017/s0013091599000772 fatcat:347tsi6rifgtzm2mgh3tzlxqsi