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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2002 • Question 2

Question

Math 6210 • Real Analysis 2002 • Question 2

Let \(P\) be a self-adjoint operator on a Hilbert space \(H\) such that \(P^2=P\). Show that \(P\) is a projection on a closed subspace. (Warning: we do not assume, apriori, that \(P\) is bounded).

Raw LaTeX

Let \(P\) be a self-adjoint operator on a Hilbert space \(H\) such that
\(P^2=P\). Show that \(P\) is a projection on a closed subspace. (Warning: we do not
assume, apriori, that \(P\) is bounded).

Topic Tags

Hilbert Spaces and Orthogonality