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Let X\, and Y\, be Banach spaces and T_{n}\in B(X,Y)\,. Show that the following are equivalent:

(a) \left\{||T_{n}||\right\}_{{n=1}}^{\infty }\, is bounded;

(b) \left\{||T_{n}x||\right\}_{{n=1}}^{\infty }\, is bounded for each x\in X\,;

(c) \left\{g\left(T_{n}x\right)||\right\}_{{n=1}}^{\infty }\, is bounded for all x\in X\, and all g\in Y'\,.