Lemma 2.31 Let (X, || - ||x), (Y, || - ||Y) be normed vector spaces and F E L(X,Y).Then||F||c(x,Y) :=|| Fæ||y =||Fx||y.suprɛX; ||r||x=1suprɛX; ||r||x<1Proof:excersises.

Answered: Image /qna-images/answer/18d32594-fa68-45f9-8d5f-ad6538ff76b1.jpg

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 rɛX; ||a||x=1 || Fæ||y = sup rƐX; ||r||x<1 || Fe||y.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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Question

Lemma 2.31 Let (X, || - ||x), (Y, || - ||Y) be normed vector spaces and F E L(X,Y).
Then
||F||c(x,Y) :=
|| Fæ||y =
||Fx||y.
sup
rɛX; ||r||x=1
sup
rɛX; ||r||x<1
Proof:
excersises.

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