Universal elements for non-linear operators and their applications

We prove that under certain topological conditions on the set of universal elements of a continuous map T acting on a topological space X, that the direct sum T and M_g is universal, where M_g is multiplication by a generating element of a compact topological group. We use this result to characterize R_+-supercyclic operators and to show that whenever T is a supercyclic operator and z_1,...,z_n are pairwise different non-zero complex numbers, then the operator z_1T\oplus ... \oplus z_n T is cyclic. The latter answers affirmatively a question of Bayart and Matheron.

Using signed digit arithmetic for low-power multiplication

Hardware implementations of arithmetic operators using signed digit arithmetic have lost some of their earlier popularity. However, SD is revisited and used to realise an efficient radix-16 generic multiplier, which has particular potential for low-power implementation. The SD multiplier algorithm reduces the number of partial products to as much as 1/4, and in initial tests reduces the estimated power consumption to only about 50% of that of the Booth multiplier. It is different from other previous high-radix methods in that it employs a novel method to generate its partial products with zero arithmetic logic.

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.