Real Algebraic and Analytic Geometry |

Tracial algebras and an embedding theorem.

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Submission: 2010, May 8.

*Abstract:
We prove that every positive trace on a countably generated $*$-algebra can be
approximated by positive traces on algebras of generic matrices. This implies that every countably
generated tracial $*$-algebra can be embedded into a metric ultraproduct of generic matrix algebras.
As a particular consequence, every finite von Neumann algebra with separable pre-dual can be embedded
into an ultraproduct of tracial $*$-algebras, which as $*$-algebras embed into a matrix-ring over a commutative algebra.*

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