Talk:Spectral theory of compact operators

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Bounded Sequences Have Weakly Convergent Subsequences?

In the proof of one of the Lemmas in the article it is used that every bounded sequence has a weakly convergent subsequence. In the Wikipedia Article Reflexive_Banach_space it is stated that this rule can only be applied in reflexive Banach spaces, so my question here is: Why are we allowed to use this fact? I know that most of the times, one is interested in compact operators on Hilbert spaces and they are clearly reflexive, but in general, I don't see why this is allowed here. --130.83.2.27 (talk) 13:31, 25 March 2013 (UTC)[reply]

Hm, you might be right there. I am going to revert to your version, pending me taking a look later. Mct mht (talk) 01:03, 26 March 2013 (UTC)[reply]

Theorem ii.)

For some reason in the theorem, the notation switches from \lambda to \lambda_i, which has not been introduced before. I guess this is just a typo, or am I overlooking something? — Preceding unsigned comment added by 2003:E6:13D8:6F00:3D7C:CA8B:1F03:8FFC (talk) 08:23, 1 July 2017 (UTC)[reply]