GENERATORS OF BOREL MEASURABLE COMMUTATIVE ALGEBRA ON COMPACT HAUSDORFF TAKING VON NEUMANN AW* OVER *-ISOMORPHISM

Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra

Let M be a type I von Neumann algebra with the center Z and a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ -measurable operators affiliated with M. We prove that any Z-linear derivation on L(M, τ) is inner and hence automatically continuous in the measure topology. If the lattice of projections from Z is atomic then any derivation on L(M, τ) is Z-linear. This implies...

Locally Compact Quantum Groups. A von Neumann Algebra Approach

In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We start with a von Neumann algebra and a comultiplication on this von Neumann algebra. We assume that there exist faithful left and right Haar weights. Then we develop the theory within this von Neumann algebra setting. In [Math. Scand. 92 (2003), 68–92] locally ...

Derivations on the Algebra of τ-Compact Operators Affiliated with a Type I von Neumann Algebra

Let M be a type I von Neumann algebra with the center Z, a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ -measurable operators affiliated with M and let S0(M, τ) be the subalgebra in L(M, τ) consisting of all operators x such that given any ε > 0 there is a projection p ∈ P(M) with τ(p) < ∞, xp ∈ M and ‖xp‖ < ε. We prove that any Z-linear derivation of S0(M, τ) is spa...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Categorical Aspects of von Neumann Algebras and AW ∗ - algebras Sander

We take a look at categorical aspects of von Neumann algebras, constructing products, coproducts, and more general limits, and colimits. We shall see that exponentials and coexponentials do not exist, but there is an adjoint to the spatial tensor product, which takes the role of coexponent. We then introduce the class of AW*-algebras and try to see to what extend these categorical constructions...