Extension of derivations in the algebra of compact operators (Q793295)

Let C(H) denote the \(C^*\)-algebra of all compact linear operators on a complex Hilbert space. We give a sufficient condition for a closed *- derivation \(\delta\) in C(H) to have a generator extension. If \(\delta\) is a closed *-derivation in C(H) which anti-commutes with an involutive *- antiautomorphism \(\alpha\) and the implementing self-adjoint operator of \(\delta\) has finite deficiency-indices, then there exists a generator \(\delta_ 0\) of a continuous action of R on C(H) which extends \(\delta\) and anti-commutes with \(\alpha\).