We have two Banach spaces \( E \) and \( F \), and a sequence of bounded linear operators \( (T_n) \) from \( E \) to \( F \). For each \( x \in E \), the sequence \( T_n x \) converges to \( T x \) in \( F \). We need to show that if \( x_n \to x \) in \( E \),
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