Well, yesterday they announced at the blog Café Matemático that there was a problem with their proof:
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Update 05/02/2013: Cowen and Gallardo say that a problem has been found in their proof and they no longer claim an answer to the invariant subspace problem.
At the congress of la Real Sociedad Matemática Española yesterday, Eva Gallarda and Carl Cowen presented an affirmative answer to the invariant subspace problem on separable Hilbert spaces. While it isn’t a Millennium Prize problem, it’s one of the big open problems in maths. As far as I can tell, it hasn’t been through any formal peer review yet, but they’re serious people and you’ve got to be quite sure about this kind of thing before announcing it at such a high-profile event.