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(Unit sphere) The sphere S(0; 1) ={x€X||| = 1} %3D in a normed space X is called the unit sphere. Show that for the norms in Prob. 6 and for the norm defined by the unit spheres look as shown in Fig. 16. ace. Banach Space 65 ||x = 1 -l|x, = 1 Fig. 16. Unit spheres in Prob. 10

(Unit sphere) The sphere S(0; 1) ={x€X||| = 1} %3D in a normed space X is called the unit sphere. Show that for the norms in Prob. 6 and for the norm defined by the unit spheres look as shown in Fig. 16. ace. Banach Space 65 ||x = 1 -l|x, = 1 Fig. 16. Unit spheres in Prob. 10

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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6. Let X be the vector space of all ordered pairs x=(§, £2), y = (n, 72), · · · of real numbers. Show that norms on X are defined by ... || ||2 = (5,²+5;²)"/2 lI제- max {lGil, I62).
Transcribed Image Text:6. Let X be the vector space of all ordered pairs x=(§, £2), y = (n, 72), · · · of real numbers. Show that norms on X are defined by ... || ||2 = (5,²+5;²)"/2 lI제- max {lGil, I62).
(Unit sphere) The sphere S(0; 1) ={x e X |||| = 1} in a normed space X is called the unit sphere. Show that for the norms in Prob. 6 and for the norm defined by %3D the unit spheres look as shown in Fig. 16. асе. Вапаch Spасе 65 ||* = 1 ||x = 1 l|x1, = 1 -l|x, = 1 Fig. 16. Unit spheres in Prob. 10
Transcribed Image Text:(Unit sphere) The sphere S(0; 1) ={x e X |||| = 1} in a normed space X is called the unit sphere. Show that for the norms in Prob. 6 and for the norm defined by %3D the unit spheres look as shown in Fig. 16. асе. Вапаch Spасе 65 ||* = 1 ||x = 1 l|x1, = 1 -l|x, = 1 Fig. 16. Unit spheres in Prob. 10
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