(a) Prove that the L and L2 norms on the vector space C[- 1, 1 ] are...

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(a) Prove that the L∞ and L2 norms on the vector space C°[- 1, 1 ] are not equivalent. Hint: Look at Exercise 3.3.41 for ideas.
(b) Can you establish a bound in either direction, i-e.. ||f||∞ ≤ C ||f||2 or ||f||2 ≤ C ||f||∞ for all ∈ C°[- 1, 1 ] for some positive constant C, C?
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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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