Talk:Invariant subspace problem

Is "complex" Hilbert space necessary?

The article describes the invariant subspace problem as pertaining to complex Hilbert spaces. But isn't the existence of a non-trivial closed invariant subspace equally unknown for a bounded linear operator on a real Hilbert space? (In fact, I wonder if the two problems might be equivalent.)Daqu (talk) 07:18, 20 June 2008 (UTC)[reply]

Okay, I see that one would need to require the real dimension to be > 2, since otherwise a rotation in the plane has no non-trivial invariant subspace. Which is like in the complex case, where the complex dimension is required to be > 1. But other than that?Daqu (talk) 18:02, 20 June 2008 (UTC)[reply]

after having seen

Perhaps it could be mentioned that Halmos gave a proof in the same issue of the same journal, after having seen a preprint of Robinson's proof using NSA. This is a well-known fact. It anyone doubts this I could try to look up some references. Katzmik (talk) 11:10, 15 December 2008 (UTC)[reply]