5.19 Consider the mapping T: L'(0,2) L'(0, 2), (Tf)(x):= f(t)dt. (i) Show that T indeed maps L'(0, 2) into L'(0, 2). (ii) Show that T is linear and bounded.

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5.19 Consider the mapping
T: L'(0,2) – L'(0, 2), (Tf)(x):= tf(t)dt.
(i) Show that T indeed maps L'0, 2) into L'(0, 2).
(ii) Show that T is linear and bounded.
Transcribed Image Text:5.19 Consider the mapping T: L'(0,2) – L'(0, 2), (Tf)(x):= tf(t)dt. (i) Show that T indeed maps L'0, 2) into L'(0, 2). (ii) Show that T is linear and bounded.
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