(c) Let X be a normed space, Z = X andfe X'. Let T X → X be defined byT (x) = f(x)z, xe X. Prove that T islinear and compact.

We have given that, X be normed space, z∈X and f∈X' where X' denote the set of all bounded linear…

Answered: Let X be a normed space, Z = X and fe…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 24CM

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Let X be a normed space, Z = X and fe X'. Let T: X → X be defined by T (x) = f(x) z, x = X. Prove that T is linear and compact.