Consider L = I – A with A : X → X is a compact linear operator in a normed space X. Show that the nullspace N(L) is a subspace of X and is closed in X.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 56E: Give an example showing that the union of two subspaces of a vector space V is not necessarily a...
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Consider L = I - A with A : X → X is a
compact linear operator in a normed space X.
Show that the nullspace N(L) is a subspace of
X and is closed in X.
Transcribed Image Text:Consider L = I - A with A : X → X is a compact linear operator in a normed space X. Show that the nullspace N(L) is a subspace of X and is closed in X.
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