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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.

Problem Statement