Spectrally bounded operators from von Neumann algebras

We prove that every unital spectrally bounded operator from a properly infinite von Neumann algebra onto a semisimple Banach algebra is a Jordan homomorphism.

Graded Relative Evidence

Relative Evidential Supports (RES) was developed and justified several years ago as a non-numeric apparatus that allows us to compare evidential supports for alternative conclusions when making a decision. An extension called Graded Relative Evidence (GRE) of the RES concept of pairwise balancing and trading-off of evidence is reported here which keeps its basic features of simplicity and perspicacity but enriches its modelling fidelity by permitting very modest and intuitive variations in degrees of outweighing (which the essentially binary RES does not). The formal justification is very simply based on linkages to RES and to the Dempster - Shafer theory of evidence. The use of the simple extension is illustrated and to a small degree further justified empirically by application to a topical scientific debate about what is called the Congo Crossover Conjecture here. This decision-making instance is chosen because of the wealth of evidence that has been accumulated on both sides of the debate and the range of evidence strengths manifested in it. The conjecture is that the advent of Aids was in the late 1950s in the Congo when a vaccine for polio was allegedly cultivated in the kidneys of chimpanzees which allowed the Aids infection to cross over to humans from primates. © 2005 Springer.

An analogue of the Magnus problem for associative algebras

We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by $n+k$ generators and $k$ relations and has an $n$-element system of generators, then this algebra is a free algebra of rank $n$.