FA11

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Let T:C[0,1]\to C[0,1]\, be defined by

(Tx)(t)=\int _{0}^{t}x(\tau )d\tau \,

(i) Show that T\, is a bounded linear operator.

(ii) Find ||T||\,.

(iii) Show that T\, is one-to-one but not onto. Find the range space of T\,.