Let $A_n(x)$ be a sequence of symmetric matrix functions that converges in $L^p(\Omega)$ to $A(x)$. Is it true that the eigenvalues of $A_n(x)$, or a subsequence of these, converge to the eigenvalues of $A(x)$ in $L^p(\Omega)$?
Does matrix convergence in $L^p$ imply convergence of the eigenvalues in $L^p$?
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linear-algebra
real-analysis
matrices
functional-analysis
eigenvalues-eigenvectors
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0@Willie Wong: Now I got it. Thanks a lot for explaining this to me! Although I now remember hearing about weak $L^p$ spaces at some time, I completely forgot about it. So convergence in weak $L^p$ is not the same as weak convergence in $L^p$, I think that is what got me confused (-; . – 2012-06-19