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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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