Assume $(A,+,.,*)$ be a complex algebra such that $(A,+,*)$ forms a Baer*-ring (where $*$ is the involution).

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?

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?