# When an AW*-algebra is a W*-algebra

In a very old book of Kaplansky "Rings of operators", on p. 123 one can find the following sentence:

It is a standing conjecture that an AW${}^\ast$-algebra is W${}^\ast$ if its center is W${}^\ast$.

I am wondering what is the current status of this conjecture.

Thank you, J.

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