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A Baer *-ring which is not embedded into $B(H)$

Assume $A$ is a complex $*$-algebra which is also a Baer*-ring.

Q. Can we concluded that there exists a Hilbert space $H$ such that $A$ is embedded in $B(H)$ as a Baer*-ring? What about when $A$ is finite dimensional?

ABB
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