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

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

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
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Let X be a normed space, z = X and f = X'. Show that T: X→ X defined by T(x) = f(x)z, XE X is linear and compact.
Transcribed Image Text:Let X be a normed space, z = X and f = X'. Show that T: X→ X defined by T(x) = f(x)z, XE X is linear and compact.
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