Exercise 2.6.18

Answers

First check that $Φ$ is a linear transformation by

Φ (f + cg) (s) = {(f + cg)}_{S} (s) = f_{S} (s) + c g_{S} (s) = (Φ (f) + cΦ (g)) (s) .

Second we know $Φ$ is injective and surjective by Exercise 2.1.34.

jephianlin

2011-06-27 00:00