Lemma 2.31 Let (X, || · ||x), (Y, || · ||Y) be normed vector spaces and F E L(X,Y).Then||Fcx,Y)supxƐX; ||x||x=1||Fx||YsupxƐX; ||x||x<1||Fx||y.Proof:excersises.

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Answered: Lemma 2.31 Let (X, || · ||x), (Y, || ·…

Lemma 2.31 Let (X, || · ||x), (Y, || · ||Y) be normed vector spaces and F E L(X,Y). Then ||F|c(x,Y) := sup xƐX; ||x|| x=1 ||Fx||y ||Fx||y. V %3D sup xƐX; ||x||x<1 Proof: excersises.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.4: Linear Programming

Problem 7E

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Question

Lemma 2.31 Let (X, || · ||x), (Y, || · ||Y) be normed vector spaces and F E L(X,Y).
Then
||Fcx,Y)
sup
xƐX; ||x||x=1
||Fx||Y
sup
xƐX; ||x||x<1
||Fx||y.
Proof:
excersises.

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