Suppose that F₁ & F₂ are closed subspaces of a Hilbert space H. Show that Fit if Fi LF₂, then F₁+F₂ is a closed subspace. Show also that Fi II need not be closed, even though F₁ & 5₂ are closed subspaces.
Suppose that F₁ & F₂ are closed subspaces of a Hilbert space H. Show that Fit if Fi LF₂, then F₁+F₂ is a closed subspace. Show also that Fi II need not be closed, even though F₁ & 5₂ are closed subspaces.
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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Transcribed Image Text:Suppose that F₁ & F₂ are closed subspaces of a Hilbert space H. Show that
if F LF₂, then F₁+F₂ is a closed subspace. Show also that FLF need
not be closed, even though F & F are closed subspaces.
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