ON CONNECTED SUBSETS OF M(2X2) WITHOUT RANK-ONE CONNECTIONS

We prove that connected subsets of M(2x2) without rank-one connections are Lipschitz graphs of mappings from subsets of a fixed two-dimensio nal subspace to its orthogonal complement. Under a weaker condition th at the set does not have rank-one connections locally, we are able to establish some global results on the set. We also establish some resul ts on Lipschitz extensions of the functions thus obtained.