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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2010 • Question 5

Question

Math 6210 • Real Analysis Fall 2010 • Question 5

Let \(H\) be a Hilbert space, \(M\) a closed subspace of \(H\), and \(x\in H\). Prove that there is a unique point \(y\in M\) which is closest to \(x\).

Raw LaTeX

Let \(H\) be a Hilbert space, \(M\) a closed subspace of \(H\), and
\(x\in H\). Prove that there is a unique point \(y\in M\) which is closest to \(x\).

Topic Tags

Hilbert Spaces and Orthogonality