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3.x+y=x+y iff y=ax for all x, yeX and for some >0

3.x+y=x+y iff y=ax for all x, yeX and for some >0

Advanced Engineering Mathematics
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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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
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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