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).

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 21EQ
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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).
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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