Elementary results concerning the connections between deductive relations and probabilistic support are given. These are used to show that Popper-Miller's result is a special case of a more general result, and that their result is not \very unexpected" as claimed. According to Popper-Miller, a purely inductively supports b only if they are \deductively independent"|but this means that :a ` b. H...

The purpose of this paper is to prove that a completely positive projection on a Hilbert space associated with a standard form of a von Neumann algebra induces the existence of a conditional expectation of the von Neumann algebra with respect to a normal state, and we consider the application to a standard form of an injective von Neumann algebra.

We generalise group algebras to other algebraic objects with bounded Hilbert space representation theory the generalised group algebras are called “host” algebras. The main property of a host algebra, is that its representation theory should be isomorphic (in the sense of the Gelfand–Raikov theorem) to a specified subset of representations of the algebraic object. Here we obtain both existence ...