Q7) (a) Let X be a Banach space and R the usual normed space. Show that ||(z, a)|| = ||||+|al is a complete norm on XR. (b) Let X be a normed space. If ro EX is such that f(ro) = 0 for all f X, prove that ro= 0.
Q7) (a) Let X be a Banach space and R the usual normed space. Show that ||(z, a)|| = ||||+|al is a complete norm on XR. (b) Let X be a normed space. If ro EX is such that f(ro) = 0 for all f X, prove that ro= 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Q7) (a) Let X be a Banach space and R the usual normed space. Show that ||(x, a)|| =
||||+ lo] is a complete norm on XR.
(b) Let X be a normed space. If ro EX is such that f(x) = 0 for all feX", prove
that o=0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F238a2119-8246-4293-b239-2395a9d898e3%2F4bf59916-f10c-4c2c-8187-b630c54920e0%2Ff3866ti_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q7) (a) Let X be a Banach space and R the usual normed space. Show that ||(x, a)|| =
||||+ lo] is a complete norm on XR.
(b) Let X be a normed space. If ro EX is such that f(x) = 0 for all feX", prove
that o=0.
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