A density theorem on the operator algebra in Pontrjagin space (Q1604234)

The author presents a partial extension of Kaplansky's density theorem to operator algebras on Pontrjagin spaces. For an operator algebra \(M\) on such a space, set \(M_1=\{A\in M\mid \sigma (A^*A)\subset K\}\), where \(K\) is the closed unit disk. Also, for a set of operators \(M\), let \(M^s\) denote its strong closure. The main results says that if \(M\) is a norm closed self-adjoint algebra of operators on a Pontrjagin space, then \((M^s)_1 \subset (M_1)^s\).