Cohyponormal operators with the single valued extension property (Q1822325)

Using a theorem of Putinar that proves that a hyponormal operator is the restriction of a generalized scalar operator, the authors show that the hyperinvariant subspace problem for cohyponormal operators can be reduced to the special case where the cohyponormal operator (1) is the compact perturbation of a normal one and (2) has the single valued extension property. This result is then used to find some sufficient conditions that ensure that a hyponormal operator has a nontrivial invariant subspace.