Explain all opection step by step.( Not use AI ) and give me a correct answer. Thank you

13. For meN, let T. : (1', || . (1, ) -> (10 , |) . (1 ) and T : (1' , 11 . 11,) - (10, 11 . 1/ ) be the bounded linear operators defined by T. (X, , X2, ...) = (41, 2, ...), [ x, jan where y; = ]x, j >n and T(X1 , X2 , ...) = (X1, X2, .. ) . Then (a) T, does not converges to T as n -> co (b) |T, - T converges to zero as n -> 00 (c) For all x ell, T, (x) - T(x)| converges to zero as n -> co (d) For each non-zero xEl , there exists a continuous linear functional g on x such that g(T, (x)) does not converge to g (T (x)) as n -0