UNIFORM EQUICONTINUITY OF SEQUENCES OF MEASURABLE OPERATORS AND NON-COMMUTATIVE ERGODIC THEOREMS

摘要

The notion of uniform equicontinuity in measure at zero for se-quences of additive maps from a normed space into the space of measurable operators associated with a semifinite von Neumann algebra is discussed. It is shown that uniform equicontinuity in measure at zero on a dense subset im-plies the uniform equicontinuity in measure at zero on the entire space, which is then applied to derive some non-commutative ergodic theorems.