 Solution

ID: past-exam-of-the-analysis-course-of-the-university-of-oxford/2011/4/b/i/solution

a, b

and

f, h \in X

a T f + b T h (n) = α_{n} (a f (n) + b h (n)) = α_{n} a f + bh (n) .

The assumed uniqueness of the function with these coefficients implies

T (a f + bh) = a T f + b T h

. Thus $T$ is linear.

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