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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 1994 • Question 5

Question

Math 6210 • Real Analysis Fall 1994 • Question 5

Prove that if \(A\) and \(B\) are closed subspaces of a Hilbert space \(H\), \(A\perp B\), then \(A+B\) is also closed in \(H\).

Raw LaTeX

Prove that if \(A\) and \(B\) are closed subspaces of a Hilbert space
\(H\), \(A\perp B\), then \(A+B\) is also closed in \(H\).

Topic Tags

Hilbert Spaces and Orthogonality