Abstract:
Let a von Neumann algebra M of operators act on a Hilbert space H
, τ be a faithful normal semifinite trace on M. Let tτl be the topology of τ-local convergence in measure on the *-algebra S(M,τ) of all τ
-measurable operators. We prove the tτl-continuity of the involution on the set of all normal operators in S(M,τ). We investigate the tτl
-continuity of operator functions on S(M,τ)
. We show that the mapping A↦|A| is tτl-continuous on the set of all partial isometries in M.
