Talk:Min-max theorem

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What happens if a positive eigenvalue occurs with multiplicity 2? Also, the statement as it stands precludes the possibility that there is no minimal strictly positive eigenvalue. I'm changing it accordingly... Lupin 15:49, 30 July 2005 (UTC)

[edit] compact operators

For infinitely dimensional spaces, there might well be only a finite number of positive eigenvalues or no eigenvalues at all, contrary to what is stated in the demonstration in the section devoted to compact operators. In this case, there is of course an infinite number of negative eigenvalues. The demonstration should be modified accordingly. For example when the number of positive eigenvalues is a finite n and Sk has k > n, then it seems to me that \max_{S_k} \min_{x\in S_k,\|x\|=1}(Ax,x) = 0. Similar considerations should apply also for negative eigenvalues. Luca.Argenti (talk) 09:23, 29 May 2008 (UTC)