3. Two vector norms 11·11 and III'lll on a if there exists Space X are equivalent C70 such that |||X| |/ ≤ ||X|| ≤ (|||X|!! xf x.
3. Two vector norms 11·11 and III'lll on a if there exists Space X are equivalent C70 such that |||X| |/ ≤ ||X|| ≤ (|||X|!! xf x.
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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Transcribed Image Text:b) show that the norms 11·11 and 111:111 art
equivalent if and only if sup{||X|||:|1x|| = I}
CAD and inf{111X/1) : 11x1) =1^²} 20₁
I prove that the notion of bring (quivalent
equivalence verlation on the
norms is an
367
of norms on X
Transcribed Image Text:3. Two
normg 11·11 and Ill·lll on
а
vector
Space X are equivalent if there exists
спо
070 such that
_ |||X| || = ||X|| = (111 all!, xf X
드
X
Expert Solution
Step 1
Definition: (Equivalence of Norms)
Two norms on a vector space "V" are said to be equivalent if they define same open subsets of "V" or in other words if they define the same topology on "V".
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