Von Neumann conjectured that the countable chain condition and the weak (ω, ω)-distributive law characterize measurable algebras among Boolean σalgebras [Mau]. Consistent counter-examples have been obtained by Maharam [Mah], Jensen [J], Glówczyński [Gl], and Veličković [V]. However, whether von Neumann’s proposed characterization of measurable algebras fails within ZFC remains an open problem. ...

The von Neumann algebra free product of arbitary finite dimensional von Neumann algebras with respect to arbitrary faithful states, at least one of which is not a trace, is found to be a type III factor possibly direct sum a finite dimensional algebra. The free product state on the type III factor is what we call an extremal almost periodic state, and has centralizer isomorphic to L(F∞). This a...

Let M be a von Neumann algebra (not necessarily semi-finite). We provide a generalization of the classical Kadec-Pe lczynski subsequence decomposition of bounded sequences in L[0, 1] to the case of the Haagerup L-spaces (1 ≤ p < ∞). In particular, we prove that if (φn)n is a bounded sequence in the predual M∗ of M, then there exist a subsequence (φnk)k of (φn)n, a decomposition φnk = yk + zk su...

We describe a Markov dilation for any weak* continuous semigroup \((T_t)_t \geqslant 0\) of selfadjoint unital completely positive Fourier multipliers acting on the group von Neumann algebra \(\mathrm {VN}(G)\) locally compact G.

We extend some inequalities for normal matrices and positive linear maps related to the Russo-Dye theorem. The results cover case of on a von Neumann algebra mapping any nonzero operator an unbounded operator.

We consider hermitian dissipative mappings δ which are densely defined in unital C∗-algebras A. The identity element in A is also in the domain of δ. Completely dissipative maps δ are defined by the requirement that the induced maps, (aij) → (δ(aij)), are dissipative on the n by n complex matrices over A for all n. We establish the existence of different types of maximal extensions of completel...

The development of quantum measurement theory, initiated by von Neumann, only indicated a possibility for resolution of the interpretational crisis of quantum mechanics. We do this by divorcing the algebra of the dynamical generators and the algebra of the actual observables, or beables. It is shown that within this approach quantum causality can be rehabilitated in the form of a superselection...

In a previous paper, we showed that every strongly commuting pair of CP0-semigroups on a von Neumann algebra (acting on a separable Hilbert space) has an E0-dilation. In this paper we show that if one restricts attention to the von Neumann algebra B(H) then the unitality assumption can be dropped, that is, we prove that every pair of strongly commuting CP-semigroups on B(H) has an E-dilation. I...