The notion of automatic selfadjointness all ideals in a multiplicative semigroup the bounded linear operators on separable Hilbert space B(H) arose 2015 discussion with Heydar Radjavi who pointed out that and finite rank F(H) possessed this unitary invariant property which category we named SI semigroups (for selfadjoint ideal semigroups). Equivalent to is solvability, for each A semigroup, bil...