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Show that the norms 11·11 and 111:111 art =cquivalent if and only if sup{||||||:|1x|| = I} CAD and inf{111X/1) : 11x1) = 1²} 20₁

Show that the norms 11·11 and 111:111 art =cquivalent if and only if sup{||||||:|1x|| = I} CAD and inf{111X/1) : 11x1) = 1²} 20₁

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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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
111.111 - topology of Ja equivalent CAD and Show that the norms 11:11 and 111.111 art if and only if sup{||||||:|1x|| = I} inf{111X11 ) | ||X|) = 1^²} 20₁ I'} (
Transcribed Image Text:111.111 - topology of Ja equivalent CAD and Show that the norms 11:11 and 111.111 art if and only if sup{||||||:|1x|| = I} inf{111X11 ) | ||X|) = 1^²} 20₁ I'} (
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