SCHWEITZER 1993 Problem 8

Let H be a complex separable Hilbert space and denote $B(H)$ the algebra of bounded linear operators on H. Find all *-subalgebras C of $B(H)$ for which for all $A \in B(H)$ and $T \in C$ there exists $S \in C$ that $$TA-AT^{\ast} = TS-ST^{\ast}$$ note: *-algebra is also known as involutive algebra.