Talk:Fredholm alternative

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Perhaps one should mention, in the statement of Fredholm's alternative, that lambda is non-zero.

[edit] adjoint

shouldnt we mention the orthagonality between the kernel of the adjoint and the range of operator

[edit] Alternative... to what?

To what is the Fredholm alternative an alternative? —Ben FrantzDale 15:50, 20 December 2006 (UTC)

not quite sure, but i don't think the article's claim that Fredholm alternative was due to Fredholm is right. Fredholm considered integral operators and it was F. Riesz who developed the general spectral theory of compact operators and, IIRC, formulated the Fredholm alternative. Mct mht 12:36, 8 April 2007 (UTC)

[edit] clean up

i would suggest that the "linear algebra" and "correspondence" section be deleted. sure, a linear map on a finite dimensional space is injective iff it's surjective. so every number in the spectrum is an eigenvalue. the Fredholm alternative says something similar about compact operators. but to say there's some correspondence with the finite dimensional case would be pushing it, IMHO. for one thing, the spectrum of a compact operator on an infinite dim Banach space must accumulate at 0. (of course the Fredholm alternative hinges crucially on the compactness assumption. one can mention this connection with the finite dimensional case, where this analytic aspect is completely surpressed.) Mct mht 15:14, 8 April 2007 (UTC)