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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2015 • Question 3

Question

Math 6210 • Real Analysis Fall 2015 • Question 3

If \(v_i\in \mathcal H\) converges weakly to \(v_\infty \) and \(\lVert v_\infty \rVert =\lim _{i\to \infty }\lVert v_i\rVert \), then does \(v_i\) converge in norm to \(v_\infty \)?

Raw LaTeX

If \(v_i\in\mathcal H\) converges weakly to \(v_\infty\) and
\(\lVert v_\infty\rVert=\lim_{i\to\infty}\lVert v_i\rVert\), then does \(v_i\)
converge in norm to \(v_\infty\)?

Topic Tags

Weak Topologies and Weak Convergence