Self-injective Von Neumann regular subrings and a theorem of Pere Menal

Stone - von Neumann theorem

The bibliography indicates the origins of these issues in proving uniqueness, up to isomorphism, of the model for the commutation rules of quantum mechanics. As Mackey and Weil observed, some form of the argument succeeds in quite general circumstances. The argument here is an amalgam and adaptation of those in sources in the bibliography. The proof here applies nearly verbatim, with suitable a...

Von Neumann Regular Cellular Automata

For any group G and any set A, a cellular automaton (CA) is a transformation of the configuration space A G defined via a finite memory set and a local function. Let CA(G; A) be the monoid of all CA over A G. In this paper, we investigate a generalisation of the inverse of a CA from the semigroup-theoretic perspective. An element τ ∈ CA(G; A) is von Neumann regular (or simply regular) if there ...

On a Theorem of Von Neumann

1. Introduction. Let 5 be a measure space with a countably additive , (T-finite, complete (non-negative) measure. J. von Neumann has proved that, from each class x of measurable sets modulo null sets of 5, a representative set R(x)Ex can be picked in such a way

On A Theorem of von Neumann.

Amenable Representations and Finite Injective Von Neumann Algebras

Let U(M) be the unitary group of a finite, injective von Neumann algebra M . We observe that any subrepresentation of a group representation into U(M) is amenable in the sense of Bekka; this yields short proofs of two known results—one by Robertson, one by Haagerup—concerning group representations into U(M). A unitary representation π of a group Γ on a Hilbert space Hπ is amenable if there exis...