Extension of derivations in the algebra of compact operators

Let C(H) denote the C¹-algebra of all compact linear operators on a complex Hilbert space H. If δ is a closable ¹-derivation in C(H) which anti-commutes with an involutive ¹-antiautomorphism α and has finite spatial deficiency-indices, then there exists an infinitesimal generator δ₀ of a continuous action of R on C(H) which extends δ and anti-commutes with α. This is an analogue of the von Neumann's theorem which states that a symmetric operator commuting with a conjugation J has a self-adjoint extension which also commutes with J.