3.x+y=x+y iff y=ax for all x, yeX and for some >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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Question
![Let X be a pre-Hilbert space. Prove or disprove
3.x+y=x+y iff y=ax for all x,yeX and for some > 0
4. x-y-x-||-||-y|| iff z=2x+(1-2)y for all x,y e X and for some 0≤2<0
5.x-y = |x|-|y|iff y=x for all x,yeX and for some >> 0
6. If x0 and (y) bounded, then (x,y) →0
7. If x→x and (x.x) → (x,x), then x →*
8. (x,y) = Re((x, y))+iRe((x,y))
9. x+y|-|xy|² = 4 Rether and som
خير
y))
10. If (x, y) ER and x||≤47 ||||≤2, then |(x, y)| ≤ 3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25c1a740-5e55-408d-9b78-b1ef8f5bd132%2F7376d96e-9eee-41d5-9baa-4512358a16ab%2Fd1262ko_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X be a pre-Hilbert space. Prove or disprove
3.x+y=x+y iff y=ax for all x,yeX and for some > 0
4. x-y-x-||-||-y|| iff z=2x+(1-2)y for all x,y e X and for some 0≤2<0
5.x-y = |x|-|y|iff y=x for all x,yeX and for some >> 0
6. If x0 and (y) bounded, then (x,y) →0
7. If x→x and (x.x) → (x,x), then x →*
8. (x,y) = Re((x, y))+iRe((x,y))
9. x+y|-|xy|² = 4 Rether and som
خير
y))
10. If (x, y) ER and x||≤47 ||||≤2, then |(x, y)| ≤ 3
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