Question: Suppose that the sequence of bounded linear operators ( T n ) n N , i.e., T n ( L ( X ) , )

Suppose that the sequence of bounded linear operators (Tn)nN, i.e., Tn(L(X),) in the Banach space X, has the following: nNTn1L(X):TnT,n(L(X),) . Suppose that (Tn1)nN is bounded in (L(X),). Show that T1L(X):Tn1T1,n(L(X),).

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