Constrained von Neumann Inequalities

A Hierarchy of Von Neumann Inequalities?

The well-known von Neumann inequality for commuting row contractions can be interpreted as saying that the tuple (Mz1 , . . . ,Mzn) on the Drury-Arveson space H 2 n dominates every other commuting row contraction (A1, . . . , An). We show that a similar domination relation exists among certain pairs of “lessor” row contractions (B1, . . . , Bn) and (A1, . . . , An). This hints at a possible hie...

Von Neumann Betti Numbers and Novikov Type Inequalities

In this paper we show that Novikov type inequalities for closed 1-forms hold with the von Neumann Betti numbers replacing the Novikov numbers. As a consequence we obtain a vanishing theorem for L cohomology. We also prove that von Neumann Betti numbers coincide with the Novikov numbers for free abelian coverings. §0. Introduction S. Novikov and M. Shubin [NS] proved that Morse inequalities for ...

Von Neumann Quantum Logic vs. Classical von Neumann Architecture?

The name of John von Neumann is common both in quantum mechanics and computer science. Are they really two absolutely unconnected areas? Many works devoted to quantum computations and communications are serious argument to suggest about existence of such a relation, but it is impossible to touch the new and active theme in a short review. In the paper are described the structures and models of ...

Nonlinear $*$-Lie higher derivations on factor von Neumann algebras

Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.

Von Neumann Symposium, MSRI