- 3 Given F B A B We Know That Inf F X X A B Exists Suppose We Define A Map By B A B R With 1 (117.91 KiB) Viewed 34 times
3. Given f € B[a, b] we know that inf{|ƒ(x)| : x = [a, b]} exists. Suppose we define a map by ||·||; : B[a, b] → R with
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3. Given f € B[a, b] we know that inf{|ƒ(x)| : x = [a, b]} exists. Suppose we define a map by ||·||; : B[a, b] → R with
3. Given f € B[a, b] we know that inf{|ƒ(x)| : x = [a, b]} exists. Suppose we define a map by ||·||; : B[a, b] → R with ||ƒ||; = inf{|ƒ(x)| : x = [a, b]}. Show that the map ||.||; is not a norm on B[a, b] NOTE: The supremum norm will be the norm to be used throughout the course unless otherwise stated.