On Uniform Equicontinuity of Sequences of Measurable Operators

The notion of uniform equicontinuity in measure at zero for sequences 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 implies the uniform equicontinuity on the entire space, which is then applied to derive some non-commutative ergodic theorems

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