Question: Let K : [0, 1]2 - IR be continuous. Show that T : C([0, 1], R) - C([0, 1], R) defined by If (x) =

Let K : [0, 1]2 - IR be continuous. Show that T : C([0, 1], R) - C([0, 1], R) defined by If (x) = K(x, y)f(y)dy o is a linear operator. That is, first show that T is well-defined by showing that If is continuous whenever f is, and then showing that T is linear

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