4 Exercise 9.8. Let X be a normed space, and let X*= (X*)* be the bidual (or doubledual) of X. Consider the map Jx : X X** defined by(Jxx)(f) = f(x),Prove that Jy is a well-defined linear isometry.r€ X, ƒ e X*.

Given: X is a normed space and X** = X** is the bidual (or double dual ) of X. Also, the map JX : X…

Answered: Exercise 9.8. Let X be a normed space,…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 6E

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Exercise 9.8. Let X be a normed space, and let X = (X*)* be the bidual (or double %3D dual) of X. Consider the map Jx: X X defined by (Jxx)(f) = f(x), Prove that Jx is a well-defined linear isometry. I€ X, ƒ € X*.

Exercise 9.8. Let X be a normed space, and let X = (X) be the bidual (or double %3D dual) of X. Consider the map Jx: X X defined by (Jxx)(f) = f(x), Prove that Jx is a well-defined linear isometry. I€ X, ƒ € X*.