Instantons on noncommutative R-4 and projection operators

The noncommutative version of ADHM construction of instantons, which was pr oposed by Nekrasov and Schwarz, is carefully studied, Noncommutative R-4 is described by an algebra of operators acting in a Fock space. In the ADHM c onstruction of instantons, one looks for zero-modes of the Dirac-like opera tor. The feature peculiar to the noncommutative case is that these zero-mod es project out some states in the Fock space. The mechanism of these projec tions is clarified in the case that the gauge group is U(1). In U(N) cases, it is shown in some explicit examples that projections similar to those in the U(1) cases also appear. A physical interpretation of these projections in the IIB matrix model is also discussed.