(a) Let A = B(X) where X is a Banach space. Suppose there exists m >0 suchthat||Ax|| ≥ m||x||, Vx € X.Show that Image A is closed in X.(b) Let A = B(H) be self adjoint, where H is a Hilbert space. Let λ = C suchthat Imλ ‡0. Prove that|| Ax − λx|| ≥ |Im\| ||x||, Vx € H.ɛ1.Prove that X is a regular point of A.

Answered: Image /qna-images/answer/341a2a92-2c67-48bd-8fbc-5f1188fd8961.jpg

Answered: (a) Let A = B(X) where X is a Banach…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 73CR

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