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Let M be a closed subspace of a Hilbert space H. Prove that MnM = {0} and that every h in H can be written uniquely as h = f +g, where f e M and gE M. %3D

Let M be a closed subspace of a Hilbert space H. Prove that MnM = {0} and that every h in H can be written uniquely as h = f +g, where f e M and gE M. %3D

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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Let M be a closed subspace of a Hilbert space H. Prove that MnM = {0} and that every h in H can be written uniquely as h = f +g, where f E M and ge M.
Transcribed Image Text:Let M be a closed subspace of a Hilbert space H. Prove that MnM = {0} and that every h in H can be written uniquely as h = f +g, where f E M and ge M.
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