Making use of its smooth structure only, out a connected oriented $4$-manifold von Neumann algebra is constructed. As special four dimensional phenomenon this approximated by algebraic (i.e., formal) curvature tensors the underlying and itself hyperfinite factor ${\rm II}_1$ type hence unique up to abstract isomorphisms algebras. Nevertheless over fixed admits representation on Hilbert space su...

We prove a generalization of the polarization identity linear algebra expressing inner product complex space in terms norm, where field scalars is extended to an associative equipped with involution, and viewed as averaging operation over compact multiplicative subgroup scalars. Using this we general form Jordan-von Neumann theorem on characterizing spaces among normed spaces, when are taken al...

Let M be a von Neumann algebra and ρ : M → M be a ∗-homomorphism. Then ρ is called a centrally extendable ∗-homomorphism (CEH) if there is a maximal abelian subalgebra (masa) M of the commutant M of M and a surjective ∗-homomorphism φ : M → M such that φ(Z) = ρ(Z) for all Z in the center of M. A ∗-ρderivation δ : M → M is called a centrally extendable ∗-ρ-derivation (CED) if there is a masa M o...

Relativizing an idea from multiplicity theory, we say that an element x of a von Neumann algebra M is n-divisible if W (x) ∩ M unitally contains a factor of type In. We decide the density of the n-divisible operators, for various n, M, and operator topologies. The most sensitive case is σ-strong density in II1 factors, which is closely related to the McDuff property. We make use of Voiculescu’s...

The present article deals with convergence in probability in L-spaces from a functional analytic point of view. The L-spaces in question are the preduals of von Neumann algebras with finite faithful normal traces. To consider an easy example we look at the commutative case: Let (Ω,Σ, μ) be a finite measure space, let (fn) be a bounded sequence in L (Ω,Σ, μ). If (appropriately chosen representat...

We show that if A is a Hilbert–space operator, then the set of all projections onto hyperinvariant subspaces of A, which is contained in the von Neumann algebra vN(A) that is generated by A, is independent of the representation of vN(A), thought of as an abstract W∗–algebra. We modify a technique of Foias, Ko, Jung and Pearcy to get a method for finding nontrivial hyperinvariant subspaces of ce...

All rings R considered are commutative and have an identity element. Contessa called R a VNL-ring if a or 1 a has a Von Neumann inverse whenever a 2 R. Sample results: Every prime ideal of a VNL-ring is contained in a unique maximal ideal. Local and Von Neumann regular rings are VNL and if the product of two rings is VNL, then both are Von Neumann regular, or one is Von Neumann regular and the ...

We consider the analogues of the Horn inequalities in finite von Neumann algebras, which concern the possible spectral distributions of sums a + b of self–adjoint elements a and b in a finite von Neumann algebra. It is an open question whether all of these Horn inequalities must hold in all finite von Neumann algebras, and this is related to Connes’ embedding problem. For each choice of integer...