Journal of the Ramanujan Mathematical Society
Volume 40, Issue 3, September 2025 pp. 215–227.
Liftable functionals and finite-dimensional factorization: non-tracial examples
Authors:
Angshuman Bhattacharya and Sagar N. Shinde
Author institution:Department of Mathematics, IISER, Bhopal, Madhya~Pradesh~462~066, India.
Summary:
Motivated by Connes and Kirchberg's liftable traces, we introduce the concept
of {liftability} for a non-tracial faithful normal state on a
von-Neumann algebra. Further we refine this notion of liftability to
{finite liftability} of a non-tracial faithful normal state. We show
by example that, injective factors of type I{∞}, II{∞}
and III{λ} (0 < λ ≤ 1) admit {finitely liftable
non-tracial} faithful normal states.
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