A JW algebra is a Jordan subalgebra of the Jordan algebra of self-adjoint operators on a complex Hilbert space that is closed in the weak operator topology .
A JW - Algebra is a Jordan - Subalgebra of the Jordan - Algebra of Self - Adjoint - operators on a complex Hilbert - space that is completed in the weak operator - topology .

Are these two sentences paraphrases of each other?
yes