For more than a century scientists have relied on the “ergodic theorem” to explain diffusive processes such as the movement of molecules in a liquid. However, they had not been able to confirm ...

A dynamical system in which repeated measurements on a single particle yield the same mean result as a single measurement of the whole ensemble is said to be ergodic. The ergodic theorem expresses a ...

This is a preview. Log in through your library . Abstract Let P1, ..., Pd be commuting positive linear contractions on L1 and let T1, ..., Td be (not necessarily commuting) linear contractions on L1 ...

We prove a nonlinear ergodic theorem for noncommutative semigroups of nonexpansive mappings in a Hilbert space. Furthermore, we give a necessary and sufficient condition for a noncommutative semigroup ...