supr.] f(t) Consider C[0, 1] with the usual supremum norm (ie. || for fe C[0, 1])....

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supr.] f(t) Consider C[0, 1] with the usual supremum norm (ie. || for fe C[0, 1]). Let T: C[0, 1] → C[0, 1] be given by T f(t) = f s7 f(s) ds. te [0,1] (here fe C[0,1]). Show (a). ||TS|C[0, 1] and (b). ||7|| = supr.] f(t) Consider C[0, 1] with the usual supremum norm (ie. || for fe C[0, 1]). Let T: C[0, 1] → C[0, 1] be given by T f(t) = f s7 f(s) ds. te [0,1] (here fe C[0,1]). Show (a). ||TS|C[0, 1] and (b). ||7|| =

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To prove that Tf 18 f for all f c01 use the definition of the supremum norm a... View the full answer