Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 1997 • Question 4

Question

Math 6210 • Real Analysis Fall 1997 • Question 4

Let \(H\) be a Hilbert space, \(M\) a closed subspace, and \(N\) a finite dimensional subspace of \(H\). Show that \(M+N\) is a closed subspace of \(H\).

Raw LaTeX

Let \(H\) be a Hilbert space, \(M\) a closed subspace, and \(N\) a finite
dimensional subspace of \(H\). Show that \(M+N\) is a closed subspace of \(H\).

Topic Tags

Hilbert Spaces and Orthogonality