If M = {x: Lx = 0}, where L is a continuous linear functional on H, prove that M¹ is a vector space of dimension 1 (unless M = H).
If M = {x: Lx = 0}, where L is a continuous linear functional on H, prove that M¹ is a vector space of dimension 1 (unless M = H).
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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![If M = {x: Lx = 0}, where L is a continuous linear
functional on H, prove that M is a vector
space of dimension 1 (unless M = H).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12664eae-ef87-4a96-a4cf-d831e7ed81ab%2F8e0d8371-d33a-4c23-96a9-ff52de10d0fe%2Fmgjk8nn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If M = {x: Lx = 0}, where L is a continuous linear
functional on H, prove that M is a vector
space of dimension 1 (unless M = H).
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