Abstract
We employ the twistor approach to the construction of
U(2) multi-instantons à la 't Hooft on
non-commutative 
4. The non-commutative deformation of the
Corrigan-Fairlie-'t Hooft-Wilczek ansatz is derived. However,
naively substituting into it the 't Hooft-type solution is
unsatisfactory because the resulting gauge field fails to be
self-dual on a finite-dimensional subspace of the Fock space. We
repair this deficiency by a suitable Murray-von Neumann
transformation after a specific projection of the gauge
potential. The proper non-commutative 't Hooft multi-instanton
field strength is given explicitly, in a singular as well as in a
regular gauge.
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