Consider the linear space C[0, 1] equipped with the norm ||f || = max |f(t)|. te[0,1] Prove that there is no inner product on C[0, 1] agreed with this norm.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 12EQ
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Consider the linear space C[0, 1] equipped with the norm
|| ||
= max f(t)|.
te[0,1)
Prove that there is no inner product on C[0, 1] agreed with this norm.
Transcribed Image Text:Consider the linear space C[0, 1] equipped with the norm || || = max f(t)|. te[0,1) Prove that there is no inner product on C[0, 1] agreed with this norm.
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