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...

In this paper an automorphism of a unital C-algebra is said to be locally inner if on any element it agrees with some inner automorphism. We make a fairly complete study of local innerness in von Neumann algebras, incorporating comparison with the pointwise innerness of Haagerup-Størmer. On some von Neumann algebras, including all with separable predual, a locally inner automorphism must be inn...

We consider a reaction-diffusion equation with Neumann boundary conditions and show that solutions to this problem may be obtained from a problem with periodic boundary conditions and equivariant under O(2) symmetry. We describe the solutions for Hopf bifurcation and mode interactions involving Hopf bifurcation, namely, steadystate/Hopf and Hopf/Hopf. Neumann boundary conditions constrain the s...

One of the most important auxiliary objects associated with an operator algebra is its state space. The two books under review describe the authors’ solutions, obtained together with H. Hanche-Olsen and B. Iochum [1], [2], [9], to the problems: What data must be added to a state space so that the operator algebra can be recovered? and Which convex sets can arise as state spaces? As that work is...