{$L\sbp$}-spaces for von Neumann algebra with reference to a faithful normal semifinite weight

Crossed Product Decompositions of a Purely Infinite Von Neumann Algebra with Faithful, Almost Periodic Weight

For M a separable, purely infinite von Neumann algebra with almost periodic weight φ, a decomposition of M as a crossed product of a semifinite von Neumann algebra by a trace–scaling action of a countable abelian group is given. Then Takasaki’s continuous decomposition of the same algebra is related to the above discrete decomposition via Takesaki’s notion of induced action, but here one induce...

A Note on Faithful Traces on a Von Neumann Algebra

It is known that a semifinite von Neumann algebra always has a faithful semifinite trace. This trace can be used, for instance, to build up a non-commutative integration and, consequently, to define non commutative L-spaces. In this note we give some techniques for constructing, starting from a family F of semifinite traces, a faithful one which is closely related to the family F. Let F = {ηα; ...

Representation of faithful normal expectations in von Neumann algebras

The Spectral Scale of a Self-Adjoint Operator in a Semifinite von Neumann Algebra

We extend Akemann, Anderson, and Weaver’s Spectral Scale definition to include selfadjoint operators from semifinite von Neumann algebras. New illustrations of spectral scales in both the finite and semifinite von Neumann settings are presented. A counterexample to a conjecture made by Akemann concerning normal operators and the geometry of the their perspective spectral scales in the finite se...

A determinant inequality and log-majorisation for operators

‎Let $lambda_1,dots,lambda_n$  be positive real numbers such that $sum_{k=1}^n lambda_k=1$. In this paper, we prove that for any positive operators $a_1,a_2,ldots, a_n$ in semifinite von Neumann algebra $M$ with faithful normal trace that $t(1)