de Branges's solution of Invariant Subspace Problem

[Vladimir Pestov]

Louis de Branges has announced a proof of the Lomonosov Conjecture,
from which is follows in particular that every bounded linear operator
on a Hilbert space has a nontrivial invariant subspace. His note
`Une preuve de la conjecture de Lomonosov' is downloadable from:

ftp://ftp.math.purdue.edu/pub/branges/analyse.ps

However, I am afraid that the proof is flawed.
My brief comment can be downloaded (as a LaTeX 2e file) from:

http://www.vuw.ac.nz/~vova/papers/flaw.tex

The Lomonosov Conjecture -- and the Invariant Subspace Problem -- still
survive, it seems.

Vladimir Pestov

School of Mathematical and Computing Sciences,
Victoria University of Wellington,
New Zealand

vladimi...@vuw.ac.nz
http://www.vuw.ac.nz/~vova/