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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.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 34E
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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: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
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
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
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